## Bao, Weizhu

Compute Distance To:
 Author ID: bao.weizhu Published as: Bao, Weizhu; Bao, WeiZhu; Bao, W. more...less Homepage: http://ww1.math.nus.edu.sg/staff.aspx?s=matbaowz
 Documents Indexed: 138 Publications since 1994 3 Contributions as Editor Co-Authors: 78 Co-Authors with 124 Joint Publications 2,979 Co-Co-Authors
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### Co-Authors

 14 single-authored 16 Cai, Yongyong 15 Han, Houde 12 Tang, Qinglin 11 Zhang, Yanzhi 9 Jin, Shi 8 Markowich, Peter Alexander 7 Su, Chunmei 6 Dong, Xuanchun 6 Zhao, Quan 6 Zhao, Xiaofei 4 Du, Qiang 4 Lim, Fong Yin 4 Ruan, Xinran 4 Shen, Jie 4 Wang, Hanquan 4 Yin, Jia 3 Carles, Rémi 3 Jaksch, Dieter 3 Jia, Xiaowei 3 Zhang, Yong 2 Chern, I-Liang 2 Feng, Yue 2 Huang, Zhongyi 2 Jiang, Shidong 2 Le Treust, Loïc 2 Li, Hailiang 2 Mauser, Norbert Julius 2 Méhats, Florian 2 Miles, Ronald N. 2 Sun, Fangfang 2 Weishäupl, Rada-Maria 2 Xu, Zhiguo 2 Zeng, Rong 2 Zheng, Chunxiong 1 Antoine, Xavier 1 Barrett, John W. 1 Bathe, Klaus-Jürgen 1 Ben Abdallah, Naoufel 1 Besse, Christophe 1 Cai, Zhenning 1 Chai, Ming-Huang 1 Chen, Lizhen 1 Chen, Rui 1 Garcke, Harald 1 Garrison, M. R. 1 Ge, Yunyi 1 Greengard, Leslie F. 1 Ha, Seung-Yeal 1 Huang, Jingfang 1 Jian, Huaiyu 1 Jiang, Xiaoyun 1 Kim, Dohyun 1 Li, Xianggui 1 Li, Yifei 1 Lin, Bo 1 Liu, Jianguo 1 Lu, Jinfu 1 Ma, Ying 1 Marahrens, Daniel 1 Mishra, Siddhartha 1 Nürnberg, Robert 1 Pareschi, Lorenzo 1 Schmeiser, Christian 1 Sheng, Changtao 1 Shi, Shaoyun 1 Srolovitz, David J. 1 Stimming, Hans Peter 1 Tang, Tao 1 Tang, Weijun 1 Wang, Shu 1 Wang, Xiaodong 1 Wang, Yan 1 Wang, Yan 1 Wei, Guowei 1 Wen, Zaiwen 1 Wu, Xinming 1 Xin, Jack X. 1 Xin, Wen 1 Yi, Wenfan 1 Zhuang, Chijie
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### Serials

 25 Journal of Computational Physics 13 SIAM Journal on Scientific Computing 10 Computer Methods in Applied Mechanics and Engineering 10 SIAM Journal on Numerical Analysis 9 Communications in Computational Physics 6 SIAM Journal on Applied Mathematics 5 Mathematics of Computation 5 Numerische Mathematik 5 Physica D 4 Journal of Computational Mathematics 4 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 3 Multiscale Modeling & Simulation 3 Communications in Mathematical Sciences 3 Kinetic and Related Models 2 Computer Physics Communications 2 IMA Journal of Numerical Analysis 2 Journal of Sound and Vibration 2 Applied Numerical Mathematics 2 Journal of Scientific Computing 2 Methods and Applications of Analysis 1 Computers & Mathematics with Applications 1 International Journal for Numerical Methods in Fluids 1 Nonlinearity 1 Applied Mathematics and Computation 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Asymptotic Analysis 1 Journal of Tsinghua University. Science and Technology 1 European Journal of Applied Mathematics 1 SIAM Journal on Mathematical Analysis 1 Journal of Mathematical Study 1 Discrete and Continuous Dynamical Systems. Series B 1 Bulletin of the Institute of Mathematics. Academia Sinica. New Series 1 Lecture Notes Series. Institute for Mathematical Sciences. National University of Singapore 1 Science China. Mathematics 1 East Asian Journal on Applied Mathematics 1 Research in the Mathematical Sciences
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### Fields

 98 Numerical analysis (65-XX) 86 Partial differential equations (35-XX) 44 Quantum theory (81-XX) 35 Statistical mechanics, structure of matter (82-XX) 25 Fluid mechanics (76-XX) 12 Mechanics of deformable solids (74-XX) 4 Calculus of variations and optimal control; optimization (49-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Ordinary differential equations (34-XX) 3 Optics, electromagnetic theory (78-XX) 2 General and overarching topics; collections (00-XX) 2 Differential geometry (53-XX) 2 Mechanics of particles and systems (70-XX) 2 Operations research, mathematical programming (90-XX) 1 History and biography (01-XX) 1 Special functions (33-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Integral transforms, operational calculus (44-XX) 1 Functional analysis (46-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

126 Publications have been cited 2,816 times in 1,088 Documents Cited by Year
Mathematical theory and numerical methods for Bose-Einstein condensation. Zbl 1266.82009
Bao, Weizhu; Cai, Yongyong
2013
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. Zbl 1006.65112
Bao, Weizhu; Jin, Shi; Markowich, Peter A.
2002
Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. Zbl 1061.82025
Bao, Weizhu; Du, Qiang
2004
Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation. Zbl 1028.82501
Bao, Weizhu; Jaksch, Dieter; Markowich, Peter A.
2003
Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1344.35130
Antoine, Xavier; Bao, Weizhu; Besse, Christophe
2013
Uniform error estimates of finite difference methods for the nonlinear Schrödinger equation with wave operator. Zbl 1246.35188
Bao, Weizhu; Cai, Yongyong
2012
Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes. Zbl 1038.65099
Bao, Weizhu; Jin, Shi; Markowich, Peter A.
2003
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. Zbl 1264.65146
Bao, Weizhu; Cai, Yongyong
2013
Ground states and dynamics of multicomponent Bose-Einstein condensates. Zbl 1062.82034
Bao, Weizhu
2004
Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1248.65087
Bao, Weizhu; Dong, Xuanchun
2012
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
2005
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. Zbl 1198.82036
Bao, Weizhu; Cai, Yongyong; Wang, Hanquan
2010
Ground, symmetric and central vortex states in rotating Bose-Einstein condensates. Zbl 1073.82004
Bao, Weizhu; Wang, Hanquan; Markowich, Peter A.
2005
Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations. Zbl 1125.65093
Bao, Weizhu; Yang, Li
2007
Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation. Zbl 1141.35052
Bao, Weizhu; Du, Qiang; Zhang, Yanzhi
2006
Ground-state solution of Bose–Einstein condensate by directly minimizing the energy functional. Zbl 1028.82500
Bao, Weizhu; Tang, Weijun
2003
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1310.65131
Bao, Weizhu; Cai, Yongyong; Zhao, Xiaofei
2014
An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity. Zbl 1054.35088
Bao, Weizhu; Jaksch, Dieter
2003
Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates. Zbl 1330.82031
Bao, Weizhu; Chern, I-Liang; Lim, Fong Yin
2006
An efficient and stable numerical method for the Maxwell–Dirac system. Zbl 1056.81080
Bao, Weizhu; Li, Xianggui
2004
The random projection method for hyperbolic conservation laws with stiff reaction terms. Zbl 0966.65073
Bao, Weizhu; Jin, Shi
2000
Numerical methods for the generalized Zakharov system. Zbl 1236.76043
Bao, Weizhu; Sun, Fangfang; Wei, Guo Wei
2003
An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates. Zbl 1160.82343
Bao, Weizhu; Wang, Hanquan
2006
Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation. Zbl 1130.82023
Zhang, Yanzhi; Bao, Weizhu; Li, Hailiang
2007
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator. Zbl 1339.35279
Bao, Weizhu; Cai, Yongyong
2014
Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction. Zbl 1290.35236
Bao, Weizhu; Cai, Yongyong
2011
A generalized-Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating Bose-Einstein condensates. Zbl 1205.82096
Bao, Weizhu; Li, Hailiang; Shen, Jie
2009
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1365.65208
Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia
2016
An exponential wave integrator sine pseudospectral method for the Klein-Gordon-Zakharov system. Zbl 1294.65095
Bao, Weizhu; Dong, Xuanchun; Zhao, Xiaofei
2013
A simple and efficient numerical method for computing the dynamics of rotating Bose–Einstein condensates via rotating Lagrangian coordinates. Zbl 1286.35213
Bao, Weizhu; Marahrens, Daniel; Tang, Qinglin; Zhang, Yanzhi
2013
Efficient and stable numerical methods for the generalized and vector Zakharov system. Zbl 1076.35114
Bao, Weizhu; Sun, Fangfang
2005
Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow. Zbl 1173.81028
Bao, Weizhu; Lim, Fong Yin
2008
Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation. Zbl 1291.35329
Bao, Weizhu; Tang, Qinglin; Xu, Zhiguo
2013
Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. Zbl 1370.81053
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2017
Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X$$_\alpha$$ model. Zbl 1160.81497
Bao, Weizhu; Mauser, N. J.; Stimming, H. P.
2003
A uniformly accurate (UA) multiscale time integrator Fourier pseudospectral method for the Klein-Gordon-Schrödinger equations in the nonrelativistic limit regime, A UA method for Klein-Gordon-schrodinger equation. Zbl 1361.65080
Bao, Weizhu; Zhao, Xiaofei
2017
Uniformly accurate multiscale time integrators for highly oscillatory second order differential equations. Zbl 1313.65180
Bao, Weizhu; Dong, Xuanchun; Zhao, Xiaofei
2014
A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates. Zbl 1149.82018
Bao, Weizhu; Wang, Hanquan
2007
Dynamics of the ground state and central vortex states in Bose-Einstein condensation. Zbl 1154.82313
Bao, Weizhu; Zhang, Yanzhi
2005
A uniformly accurate multiscale time integrator spectral method for the Klein-Gordon-Zakharov system in the high-plasma-frequency limit regime. Zbl 1373.82086
Bao, Weizhu; Zhao, Xiaofei
2016
A regularized Newton method for computing ground states of Bose-Einstein condensates. Zbl 1433.82025
Wu, Xinming; Wen, Zaiwen; Bao, Weizhu
2017
Error estimates for the finite element approximation of problems in unbounded domains. Zbl 1001.65118
Han, Houde; Bao, Weizhu
2000
Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates. Zbl 1335.35227
Bao, Weizhu; Cai, Yongyong
2015
Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars. Zbl 1220.83023
Bao, Weizhu; Dong, Xuanchun
2011
Mathematical models and numerical methods for Bose-Einstein condensation. Zbl 1373.35283
Bao, Weizhu
2014
A parametric finite element method for solid-state dewetting problems with anisotropic surface energies. Zbl 1378.76043
Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan
2017
A discrete artificial boundary condition for steady incompressible viscous flows in a no-slip channel using a fast iterative method. Zbl 0810.76052
Han, Houde; Lu, Jinfu; Bao, Weizhu
1994
A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. Zbl 1149.76039
Bao, Weizhu; Shen, Jie
2008
Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse. Zbl 1190.35205
Bao, Weizhu; Dong, Xuanchun; Xin, Jack
2010
Efficient numerical methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations. Zbl 1349.82069
Bao, Weizhu; Chern, I-Liang; Zhang, Yanzhi
2013
Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation. Zbl 1416.35225
Bao, Weizhu; Carles, Rémi; Su, Chunmei; Tang, Qinglin
2019
Fast and accurate evaluation of nonlocal Coulomb and dipole-dipole interactions via the nonuniform FFT. Zbl 1307.65184
Jiang, Shidong; Greengard, Leslie; Bao, Weizhu
2014
A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime. Zbl 1346.35171
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2016
An artificial boundary condition for two-dimensional incompressible viscous flows using the method of lines. Zbl 0865.76062
Han, Houde; Bao, Weizhu
1996
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation. Zbl 1202.35311
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
2007
A priori and a posteriori error bounds for a nonconforming linear finite element approximation of a non-Newtonian flow. Zbl 0912.76025
Bao, Weizhu; Barrett, John W.
1998
An artificial boundary condition for the incompressible viscous flows in a no-slip channel. Zbl 0818.76067
Han, Houde; Bao, Weizhu
1995
The random projection method for stiff detonation capturing. Zbl 0997.80013
Bao, Weizhu; Jin, Shi
2001
The random projection method for stiff multispecies detonation capturing. Zbl 1017.76073
Bao, Weizhu; Jin, Shi
2002
Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement. Zbl 1246.35187
Bao, Weizhu; Ben Abdallah, Naoufel; Cai, Yongyong
2012
Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT. Zbl 1388.65115
Bao, Weizhu; Tang, Qinglin; Zhang, Yong
2016
The dynamics and interaction of quantized vortices in the Ginzburg-Landau-Schrödinger equation. Zbl 1220.35165
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
2007
Stable equilibria of anisotropic particles on substrates: a generalized Winterbottom construction. Zbl 1386.74059
Bao, Weizhu; Jiang, Wei; Srolovitz, David J.; Wang, Yan
2017
Numerical simulation for the problem of infinite elastic foundation. Zbl 0896.73058
Han, Houde; Bao, Weizhu; Wang, Tao
1997
Numerical methods for the nonlinear Schrödinger equation with nonzero far-field conditions. Zbl 1090.65116
Bao, Weizhu
2004
Singular limits of Klein-Gordon-Schrödinger equations to Schrödinger-Yukawa equations. Zbl 1210.35223
Bao, Weizhu; Dong, Xuanchun; Wang, Shu
2010
Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT. Zbl 1354.65200
Bao, Weizhu; Jiang, Shidong; Tang, Qinglin; Zhang, Yong
2015
Regularized numerical methods for the logarithmic Schrödinger equation. Zbl 07114287
Bao, Weizhu; Carles, Rémi; Su, Chunmei; Tang, Qinglin
2019
The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines. Zbl 0949.65127
Han, Houde; Bao, Weizhu
1999
High-order local artificial boundary conditions for problems in unbounded domains. Zbl 0957.65096
Bao, Weizhu; Han, Houde
2000
Dimension reduction of the Schrödinger equation with Coulomb and anisotropic confining potentials. Zbl 1294.35130
Bao, Weizhu; Jian, Huaiyu; Mauser, Norbert J.; Zhang, Yong
2013
A parametric finite element method for solid-state dewetting problems in three dimensions. Zbl 1430.74056
Zhao, Quan; Jiang, Wei; Bao, Weizhu
2020
Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1453.65278
Bao, Weizhu; Zhao, Xiaofei
2019
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation. Zbl 1433.65234
Bao, Weizhu; Yin, Jia
2019
Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime. Zbl 1387.65082
Bao, Weizhu; Su, Chunmei
2018
An economical finite element approximation of generalized Newtonian flows. Zbl 1101.76351
Bao, Weizhu
2002
Dynamics of the center of mass in rotating Bose-Einstein condensates. Zbl 1190.82049
Zhang, Yanzhi; Bao, Weizhu
2007
On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments. Zbl 1075.35073
Bao, Weizhu; Markowich, Peter A.; Schmeiser, Christian; Weishäupl, Rada M.
2005
Numerical study of quantized vortex interactions in the nonlinear Schrödinger equation on bounded domains. Zbl 1320.35317
Bao, Weizhu; Tang, Qinglin
2014
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. Zbl 1440.35286
Bao, Weizhu; Cai, Yongyong; Yin, Jia
2020
Sharp-interface model for simulating solid-state dewetting in three dimensions. Zbl 1440.74153
Jiang, Wei; Zhao, Quan; Bao, Weizhu
2020
Long time error analysis of finite difference time domain methods for the nonlinear Klein-Gordon equation with weak nonlinearity. Zbl 07418058
Bao, Weizhu; Feng, Yue; Yi, Wenfan
2019
Nonlocal artificial boundary conditions for the incompressible viscous flow in a channel using spectral techniques. Zbl 0853.76054
Bao, Weizhu; Han, Houde
1996
Error estimates for the finite element approximation of linear elastic equations in an unbounded domain. Zbl 0997.74060
Han, Houde; Bao, Weizhu
2001
Numerical study of quantized vortex interaction in the Ginzburg-Landau equation on bounded domains. Zbl 1388.65046
Bao, Weizhu; Tang, Qinglin
2013
Dynamical laws of the coupled Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates. Zbl 1206.35225
Bao, Weizhu; Zhang, Yanzhi
2010
A uniformly and optimally accurate method for the Zakharov system in the subsonic limit regime. Zbl 1390.35317
Bao, Weizhu; Su, Chunmei
2018
The artificial boundary conditions for incompressible materials in an unbounded domain. Zbl 0892.73062
Han, H.; Bao, W.
1997
Weakly compressible high-order $$I$$-stable central difference schemes for incompressible viscous flows. Zbl 1054.76060
Bao, Weizhu; Jin, Shi
2001
The nonlinear Schrödinger equation and applications in Bose-Einstein condensation and plasma physics. Zbl 1140.82037
Bao, Weizhu
2007
Quantized vortex stability and interaction in the nonlinear wave equation. Zbl 1147.82037
Bao, Weizhu; Zeng, Rong; Zhang, Yanzhi
2008
A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems. Zbl 1364.81015
Bao, Weizhu; Chai, Ming-Huang
2008
A structure-preserving parametric finite element method for surface diffusion. Zbl 07423173
Bao, Weizhu; Zhao, Quan
2021
The direct method of lines for the problem of infinite elastic foundation. Zbl 0947.74076
Bao, Weizhu; Han, Houde
1999
Approximation and comparison for motion by mean curvature with intersection points. Zbl 1049.65012
Bao, Weizhu
2003
Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation. Zbl 1106.82344
Bao, Weizhu; Pareschi, Lorenzo; Markowich, Peter A.
2004
Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime. Zbl 1132.82003
Bao, Weizhu; Lim, Fong Yin; Zhang, Yanzhi
2007
A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities. Zbl 1164.78320
Bao, Weizhu; Zheng, Chunxiong
2007
Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. Zbl 1362.35278
Bao, Weizhu; Le Treust, Loïc; Méhats, Florian
2017
On the inf-sup condition of mixed finite element formulations for acoustic fluids. Zbl 1018.76023
Bao, Weizhu; Wang, Xiaodong; Bathe, Klaus-Jürgen
2001
Uniform error bounds of time-splitting spectral methods for the long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity. Zbl 07473345
Bao, Weizhu; Feng, Yue; Su, Chunmei
2022
A structure-preserving parametric finite element method for surface diffusion. Zbl 07423173
Bao, Weizhu; Zhao, Quan
2021
Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential. Zbl 1462.35318
Bao, Weizhu; Cai, Yongyong; Yin, Jia
2021
A parametric finite element method for solid-state dewetting problems in three dimensions. Zbl 1430.74056
Zhao, Quan; Jiang, Wei; Bao, Weizhu
2020
Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime. Zbl 1440.35286
Bao, Weizhu; Cai, Yongyong; Yin, Jia
2020
Sharp-interface model for simulating solid-state dewetting in three dimensions. Zbl 1440.74153
Jiang, Wei; Zhao, Quan; Bao, Weizhu
2020
An efficient and accurate MPI-based parallel simulator for streamer discharges in three dimensions. Zbl 1453.65255
Lin, Bo; Zhuang, Chijie; Cai, Zhenning; Zeng, Rong; Bao, Weizhu
2020
Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation. Zbl 1416.35225
Bao, Weizhu; Carles, Rémi; Su, Chunmei; Tang, Qinglin
2019
Regularized numerical methods for the logarithmic Schrödinger equation. Zbl 07114287
Bao, Weizhu; Carles, Rémi; Su, Chunmei; Tang, Qinglin
2019
Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1453.65278
Bao, Weizhu; Zhao, Xiaofei
2019
A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation. Zbl 1433.65234
Bao, Weizhu; Yin, Jia
2019
Long time error analysis of finite difference time domain methods for the nonlinear Klein-Gordon equation with weak nonlinearity. Zbl 07418058
Bao, Weizhu; Feng, Yue; Yi, Wenfan
2019
Computing ground states of Bose-Einstein condensates with higher order interaction via a regularized density function formulation. Zbl 1439.35436
Bao, Weizhu; Ruan, Xinran
2019
Collective synchronization of the multi-component Gross-Pitaevskii-Lohe system. Zbl 1453.35027
Bao, Weizhu; Ha, Seung-Yeal; Kim, Dohyun; Tang, Qinglin
2019
Fundamental gaps of the fractional Schrödinger operator. Zbl 1429.35195
Bao, Weizhu; Ruan, Xinran; Shen, Jie; Sheng, Changtao
2019
Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime. Zbl 1387.65082
Bao, Weizhu; Su, Chunmei
2018
A uniformly and optimally accurate method for the Zakharov system in the subsonic limit regime. Zbl 1390.35317
Bao, Weizhu; Su, Chunmei
2018
Uniform error estimates of a finite difference method for the Klein-Gordon-Schrödinger system in the nonrelativistic and massless limit regimes. Zbl 1405.65093
Bao, Weizhu; Su, Chunmei
2018
Mathematical models and numerical methods for spinor Bose-Einstein condensates. Zbl 1475.65064
Bao, Weizhu; Cai, Yongyong
2018
Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime. Zbl 1370.81053
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2017
A uniformly accurate (UA) multiscale time integrator Fourier pseudospectral method for the Klein-Gordon-Schrödinger equations in the nonrelativistic limit regime, A UA method for Klein-Gordon-schrodinger equation. Zbl 1361.65080
Bao, Weizhu; Zhao, Xiaofei
2017
A regularized Newton method for computing ground states of Bose-Einstein condensates. Zbl 1433.82025
Wu, Xinming; Wen, Zaiwen; Bao, Weizhu
2017
A parametric finite element method for solid-state dewetting problems with anisotropic surface energies. Zbl 1378.76043
Bao, Weizhu; Jiang, Wei; Wang, Yan; Zhao, Quan
2017
Stable equilibria of anisotropic particles on substrates: a generalized Winterbottom construction. Zbl 1386.74059
Bao, Weizhu; Jiang, Wei; Srolovitz, David J.; Wang, Yan
2017
Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime. Zbl 1362.35278
Bao, Weizhu; Le Treust, Loïc; Méhats, Florian
2017
Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime. Zbl 1365.65208
Bao, WeiZhu; Cai, YongYong; Jia, XiaoWei; Yin, Jia
2016
A uniformly accurate multiscale time integrator spectral method for the Klein-Gordon-Zakharov system in the high-plasma-frequency limit regime. Zbl 1373.82086
Bao, Weizhu; Zhao, Xiaofei
2016
A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime. Zbl 1346.35171
Bao, Weizhu; Cai, Yongyong; Jia, Xiaowei; Tang, Qinglin
2016
Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT. Zbl 1388.65115
Bao, Weizhu; Tang, Qinglin; Zhang, Yong
2016
The kinematic effects of the defects in liquid crystal dynamics. Zbl 1373.76011
Chen, Rui; Bao, Weizhu; Zhang, Hui
2016
Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates. Zbl 1335.35227
Bao, Weizhu; Cai, Yongyong
2015
Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT. Zbl 1354.65200
Bao, Weizhu; Jiang, Shidong; Tang, Qinglin; Zhang, Yong
2015
Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime. Zbl 1308.35263
Bao, Weizhu; Le Treust, Loïc; Méhats, Florian
2015
A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1310.65131
Bao, Weizhu; Cai, Yongyong; Zhao, Xiaofei
2014
Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrödinger equation with wave operator. Zbl 1339.35279
Bao, Weizhu; Cai, Yongyong
2014
Uniformly accurate multiscale time integrators for highly oscillatory second order differential equations. Zbl 1313.65180
Bao, Weizhu; Dong, Xuanchun; Zhao, Xiaofei
2014
Mathematical models and numerical methods for Bose-Einstein condensation. Zbl 1373.35283
Bao, Weizhu
2014
Fast and accurate evaluation of nonlocal Coulomb and dipole-dipole interactions via the nonuniform FFT. Zbl 1307.65184
Jiang, Shidong; Greengard, Leslie; Bao, Weizhu
2014
Numerical study of quantized vortex interactions in the nonlinear Schrödinger equation on bounded domains. Zbl 1320.35317
Bao, Weizhu; Tang, Qinglin
2014
Mathematical theory and numerical methods for Bose-Einstein condensation. Zbl 1266.82009
Bao, Weizhu; Cai, Yongyong
2013
Computational methods for the dynamics of the nonlinear Schrödinger/Gross-Pitaevskii equations. Zbl 1344.35130
Antoine, Xavier; Bao, Weizhu; Besse, Christophe
2013
Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation. Zbl 1264.65146
Bao, Weizhu; Cai, Yongyong
2013
An exponential wave integrator sine pseudospectral method for the Klein-Gordon-Zakharov system. Zbl 1294.65095
Bao, Weizhu; Dong, Xuanchun; Zhao, Xiaofei
2013
A simple and efficient numerical method for computing the dynamics of rotating Bose–Einstein condensates via rotating Lagrangian coordinates. Zbl 1286.35213
Bao, Weizhu; Marahrens, Daniel; Tang, Qinglin; Zhang, Yanzhi
2013
Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrödinger equation. Zbl 1291.35329
Bao, Weizhu; Tang, Qinglin; Xu, Zhiguo
2013
Efficient numerical methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations. Zbl 1349.82069
Bao, Weizhu; Chern, I-Liang; Zhang, Yanzhi
2013
Dimension reduction of the Schrödinger equation with Coulomb and anisotropic confining potentials. Zbl 1294.35130
Bao, Weizhu; Jian, Huaiyu; Mauser, Norbert J.; Zhang, Yong
2013
Numerical study of quantized vortex interaction in the Ginzburg-Landau equation on bounded domains. Zbl 1388.65046
Bao, Weizhu; Tang, Qinglin
2013
Uniform error estimates of finite difference methods for the nonlinear Schrödinger equation with wave operator. Zbl 1246.35188
Bao, Weizhu; Cai, Yongyong
2012
Analysis and comparison of numerical methods for the Klein-Gordon equation in the nonrelativistic limit regime. Zbl 1248.65087
Bao, Weizhu; Dong, Xuanchun
2012
Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement. Zbl 1246.35187
Bao, Weizhu; Ben Abdallah, Naoufel; Cai, Yongyong
2012
Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction. Zbl 1290.35236
Bao, Weizhu; Cai, Yongyong
2011
Numerical methods for computing ground states and dynamics of nonlinear relativistic Hartree equation for boson stars. Zbl 1220.83023
Bao, Weizhu; Dong, Xuanchun
2011
Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates. Zbl 1198.82036
Bao, Weizhu; Cai, Yongyong; Wang, Hanquan
2010
Comparisons between sine-Gordon and perturbed nonlinear Schrödinger equations for modeling light bullets beyond critical collapse. Zbl 1190.35205
Bao, Weizhu; Dong, Xuanchun; Xin, Jack
2010
Singular limits of Klein-Gordon-Schrödinger equations to Schrödinger-Yukawa equations. Zbl 1210.35223
Bao, Weizhu; Dong, Xuanchun; Wang, Shu
2010
Dynamical laws of the coupled Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates. Zbl 1206.35225
Bao, Weizhu; Zhang, Yanzhi
2010
A generalized-Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating Bose-Einstein condensates. Zbl 1205.82096
Bao, Weizhu; Li, Hailiang; Shen, Jie
2009
Analysis and computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation. Zbl 1186.65146
Bao, Weizhu; Lim, Fong Yin
2009
Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow. Zbl 1173.81028
Bao, Weizhu; Lim, Fong Yin
2008
A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates. Zbl 1149.76039
Bao, Weizhu; Shen, Jie
2008
Quantized vortex stability and interaction in the nonlinear wave equation. Zbl 1147.82037
Bao, Weizhu; Zeng, Rong; Zhang, Yanzhi
2008
A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems. Zbl 1364.81015
Bao, Weizhu; Chai, Ming-Huang
2008
Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates. Zbl 1159.35404
Bao, Weizhu
2008
Efficient and accurate numerical methods for the Klein-Gordon-Schrödinger equations. Zbl 1125.65093
Bao, Weizhu; Yang, Li
2007
Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation. Zbl 1130.82023
Zhang, Yanzhi; Bao, Weizhu; Li, Hailiang
2007
A mass and magnetization conservative and energy-diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates. Zbl 1149.82018
Bao, Weizhu; Wang, Hanquan
2007
Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrödinger equation. Zbl 1202.35311
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
2007
The dynamics and interaction of quantized vortices in the Ginzburg-Landau-Schrödinger equation. Zbl 1220.35165
Zhang, Yanzhi; Bao, Weizhu; Du, Qiang
2007
Dynamics of the center of mass in rotating Bose-Einstein condensates. Zbl 1190.82049
Zhang, Yanzhi; Bao, Weizhu
2007
The nonlinear Schrödinger equation and applications in Bose-Einstein condensation and plasma physics. Zbl 1140.82037
Bao, Weizhu
2007
Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime. Zbl 1132.82003
Bao, Weizhu; Lim, Fong Yin; Zhang, Yanzhi
2007
A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities. Zbl 1164.78320
Bao, Weizhu; Zheng, Chunxiong
2007
Convergence rate of dimension reduction in Bose-Einstein condensates. Zbl 1196.82065
Bao, Weizhu; Ge, Yunyi; Jaksch, Dieter; Markowich, Peter A.; Weishäupl, Rada M.
2007
Ground states and dynamics of rotating Bose-Einstein condensates. Zbl 1118.82027
Bao, Weizhu
2007
Dynamics in models of coarsening, coagulation, condensation and quantization. Zbl 1119.82003
2007
Dynamics of rotating Bose-Einstein condensates and its efficient and accurate numerical computation. Zbl 1141.35052
Bao, Weizhu; Du, Qiang; Zhang, Yanzhi
2006
Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates. Zbl 1330.82031
Bao, Weizhu; Chern, I-Liang; Lim, Fong Yin
2006
An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates. Zbl 1160.82343
Bao, Weizhu; Wang, Hanquan
2006
A fourth-order time-splitting Laguerre-Hermite pseudospectral method for Bose-Einstein condensates. Zbl 1084.35083
Bao, Weizhu; Shen, Jie
2005
Ground, symmetric and central vortex states in rotating Bose-Einstein condensates. Zbl 1073.82004
Bao, Weizhu; Wang, Hanquan; Markowich, Peter A.
2005
Efficient and stable numerical methods for the generalized and vector Zakharov system. Zbl 1076.35114
Bao, Weizhu; Sun, Fangfang
2005
Dynamics of the ground state and central vortex states in Bose-Einstein condensation. Zbl 1154.82313
Bao, Weizhu; Zhang, Yanzhi
2005
On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments. Zbl 1075.35073
Bao, Weizhu; Markowich, Peter A.; Schmeiser, Christian; Weishäupl, Rada M.
2005
Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow. Zbl 1061.82025
Bao, Weizhu; Du, Qiang
2004
Ground states and dynamics of multicomponent Bose-Einstein condensates. Zbl 1062.82034
Bao, Weizhu
2004
An efficient and stable numerical method for the Maxwell–Dirac system. Zbl 1056.81080
Bao, Weizhu; Li, Xianggui
2004
Numerical methods for the nonlinear Schrödinger equation with nonzero far-field conditions. Zbl 1090.65116
Bao, Weizhu
2004
Quantum kinetic theory: modelling and numerics for Bose-Einstein condensation. Zbl 1106.82344
Bao, Weizhu; Pareschi, Lorenzo; Markowich, Peter A.
2004
Numerical solution of the Gross–Pitaevskii equation for Bose–Einstein condensation. Zbl 1028.82501
Bao, Weizhu; Jaksch, Dieter; Markowich, Peter A.
2003
Numerical study of time-splitting spectral discretizations of nonlinear Schrödinger equations in the semiclassical regimes. Zbl 1038.65099
Bao, Weizhu; Jin, Shi; Markowich, Peter A.
2003
Ground-state solution of Bose–Einstein condensate by directly minimizing the energy functional. Zbl 1028.82500
Bao, Weizhu; Tang, Weijun
2003
An explicit unconditionally stable numerical method for solving damped nonlinear Schrödinger equations with a focusing nonlinearity. Zbl 1054.35088
Bao, Weizhu; Jaksch, Dieter
2003
Numerical methods for the generalized Zakharov system. Zbl 1236.76043
Bao, Weizhu; Sun, Fangfang; Wei, Guo Wei
2003
Effective one particle quantum dynamics of electrons: a numerical study of the Schrödinger-Poisson-X$$_\alpha$$ model. Zbl 1160.81497
Bao, Weizhu; Mauser, N. J.; Stimming, H. P.
2003
Approximation and comparison for motion by mean curvature with intersection points. Zbl 1049.65012
Bao, Weizhu
2003
Error bounds for the finite element approximation of an incompressible material in an unbounded domain. Zbl 1106.74406
Bao, Weizhu; Han, Houde
2003
High-order $$I$$-stable centered difference schemes for viscous compressible flows. Zbl 1086.76052
Bao, Weizhu; Jin, Shi
2003
Error bounds for the finite-element approximation of the exterior Stokes equations in two dimensions. Zbl 1019.65084
Bao, Weizhu
2003
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime. Zbl 1006.65112
Bao, Weizhu; Jin, Shi; Markowich, Peter A.
2002
...and 26 more Documents
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### Cited by 1,272 Authors

 69 Bao, Weizhu 27 Antoine, Xavier 27 Wang, Tingchun 27 Zhang, Luming 25 Jin, Shi 23 Cai, Yongyong 21 Lorin, Emmanuel 19 Han, Houde 18 Wang, Yushun 17 Chien, Cheng-Sheng 17 Li, Xianggui 17 Tang, Qinglin 17 Wang, Hanquan 17 Zhao, Xiaofei 13 Huang, Zhongyi 13 Schratz, Katharina 12 Markowich, Peter Alexander 12 Méhats, Florian 12 Su, Chunmei 12 Zhang, Yong 12 Zheng, Chunxiong 11 Shi, Dongyang 11 Sparber, Christof 11 Thalhammer, Mechthild 11 Zeng, Xiaoyu 11 Zhao, Qiang 10 Guo, Yujin 10 Kong, Linghua 10 Lakoba, Taras I. 10 Zhang, Yanzhi 9 Carles, Rémi 9 Dehghan Takht Fooladi, Mehdi 9 Jeng, B.-W. 9 Mei, Liquan 9 Shen, Jie 9 Song, Songhe 9 Wang, Junjun 9 Xiao, Aiguo 9 Yin, Jia 9 Zhang, Zhiyue 8 Caliari, Marco 8 Dong, Xuanchun 8 Henning, Patrick 8 Huang, Chengming 8 Liu, Zuhan 8 Qian, Xu 8 Shieh, Shih-Feng 8 Yang, Xu 8 Zhang, Jiwei 8 Zhao, Quan 8 Zhou, Huan-Song 7 Besse, Christophe 7 Cai, Jiaxiang 7 Cai, Wenjun 7 Guo, Boling 7 Ji, Bingquan 7 Jiang, Chaolong 7 Koch, Othmar 7 Li, Meng 7 Liang, Dong 7 Liao, Feng 7 Lin, Wen-Wei 7 Liu, Hailiang 7 Wu, Xinyuan 7 Xie, Jianqiang 7 Zhou, Zhennan 6 Auzinger, Winfried 6 Bandrauk, André D. 6 Chang, Shing-Lin 6 Chern, I-Liang 6 Duboscq, Romain 6 Feng, Yue 6 Gosse, Laurent 6 Huang, Yunqing 6 Li, Haochen 6 Li, Jiyong 6 Ostermann, Alexander 6 Wang, Pengde 6 Wang, Shanshan 6 Wang, Weichung 6 Wei, Juncheng 6 Xu, Zhiguo 6 Zhu, Shihui 5 Antonelli, Paolo 5 Chartier, Philippe 5 Feng, Binhua 5 Fillion-Gourdeau, François 5 Gao, Yali 5 Hajaiej, Hichem 5 Kuo, Yueh-Cheng 5 Lemou, Mohammed 5 Li, Buyang 5 Li, Zi-Cai 5 Lu, Jianfeng 5 Mauser, Norbert Julius 5 Peterseim, Daniel 5 Ruan, Xinran 5 Wang, Jianyun 5 Wang, Lan 5 Wang, Yan ...and 1,172 more Authors
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### Cited in 174 Serials

 150 Journal of Computational Physics 57 Applied Numerical Mathematics 54 Journal of Scientific Computing 52 Applied Mathematics and Computation 47 Journal of Computational and Applied Mathematics 32 Computers & Mathematics with Applications 27 Physica D 24 Computer Physics Communications 24 International Journal of Computer Mathematics 22 Numerical Algorithms 22 SIAM Journal on Scientific Computing 20 Mathematics of Computation 20 Communications in Computational Physics 18 Numerische Mathematik 18 SIAM Journal on Numerical Analysis 17 Computer Methods in Applied Mechanics and Engineering 17 Journal of Mathematical Physics 17 Applied Mathematics Letters 15 Journal of Mathematical Analysis and Applications 14 Multiscale Modeling & Simulation 13 Numerical Methods for Partial Differential Equations 13 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 13 Advances in Computational Mathematics 12 International Journal of Theoretical Physics 11 Mathematics and Computers in Simulation 11 Communications in Nonlinear Science and Numerical Simulation 11 East Asian Journal on Applied Mathematics 10 Journal of Differential Equations 10 Discrete and Continuous Dynamical Systems. Series B 10 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 10 Science China. Mathematics 9 Advances in Applied Mathematics and Mechanics 8 BIT 8 Calculus of Variations and Partial Differential Equations 8 Discrete and Continuous Dynamical Systems 6 Computers and Fluids 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 Kinetic and Related Models 5 ZAMP. Zeitschrift für angewandte Mathematik und Physik 5 Calcolo 5 SIAM Journal on Matrix Analysis and Applications 5 Applied Mathematical Modelling 5 SIAM Journal on Mathematical Analysis 5 Boundary Value Problems 4 Archive for Rational Mechanics and Analysis 4 Mathematical Methods in the Applied Sciences 4 Nonlinearity 4 Journal of Functional Analysis 4 Journal of Computational Mathematics 4 SIAM Journal on Applied Mathematics 4 Journal of Nonlinear Science 4 Computational and Applied Mathematics 4 Chaos 4 Foundations of Computational Mathematics 4 Discrete and Continuous Dynamical Systems. Series S 4 Electronic Research Archive 3 Applicable Analysis 3 Communications in Mathematical Physics 3 Physics Letters. A 3 Wave Motion 3 Acta Applicandae Mathematicae 3 Japan Journal of Industrial and Applied Mathematics 3 Discrete Dynamics in Nature and Society 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Advances in Difference Equations 3 Frontiers of Mathematics in China 3 Advances in Mathematical Physics 2 Letters in Mathematical Physics 2 Studies in Applied Mathematics 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 Acta Mathematicae Applicatae Sinica. English Series 2 Mathematical and Computer Modelling 2 Communications in Partial Differential Equations 2 Journal of Dynamics and Differential Equations 2 Communications in Numerical Methods in Engineering 2 Engineering Analysis with Boundary Elements 2 Mathematical Problems in Engineering 2 Journal of High Energy Physics 2 Living Reviews in Relativity 2 International Journal of Nonlinear Sciences and Numerical Simulation 2 Nonlinear Analysis. Real World Applications 2 Nonlinear Analysis. Modelling and Control 2 Journal of Applied Mathematics 2 Journal of Applied Mathematics and Computing 2 International Journal of Computational Methods 2 Journal of Hyperbolic Differential Equations 2 Acta Mechanica Sinica 2 Research in the Mathematical Sciences 2 AMM. Applied Mathematics and Mechanics. (English Edition) 1 International Journal of Modern Physics B 1 Bulletin of the Australian Mathematical Society 1 International Journal of Heat and Mass Transfer 1 Journal of Mathematical Biology 1 Physica A 1 Physics Reports 1 Arkiv för Matematik 1 Chaos, Solitons and Fractals 1 Advances in Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Applied Mathematics and Optimization ...and 74 more Serials
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### Cited in 44 Fields

 782 Numerical analysis (65-XX) 775 Partial differential equations (35-XX) 201 Quantum theory (81-XX) 182 Statistical mechanics, structure of matter (82-XX) 107 Fluid mechanics (76-XX) 47 Optics, electromagnetic theory (78-XX) 41 Dynamical systems and ergodic theory (37-XX) 39 Mechanics of deformable solids (74-XX) 29 Calculus of variations and optimal control; optimization (49-XX) 27 Ordinary differential equations (34-XX) 24 Classical thermodynamics, heat transfer (80-XX) 16 Real functions (26-XX) 14 Approximations and expansions (41-XX) 12 Operator theory (47-XX) 12 Probability theory and stochastic processes (60-XX) 10 Operations research, mathematical programming (90-XX) 9 Computer science (68-XX) 9 Biology and other natural sciences (92-XX) 8 Special functions (33-XX) 7 Functional analysis (46-XX) 7 Astronomy and astrophysics (85-XX) 6 Mechanics of particles and systems (70-XX) 6 Relativity and gravitational theory (83-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Difference and functional equations (39-XX) 4 Harmonic analysis on Euclidean spaces (42-XX) 4 Integral equations (45-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Information and communication theory, circuits (94-XX) 3 Combinatorics (05-XX) 3 Statistics (62-XX) 2 Group theory and generalizations (20-XX) 2 Differential geometry (53-XX) 2 Systems theory; control (93-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Category theory; homological algebra (18-XX) 1 Measure and integration (28-XX) 1 Potential theory (31-XX) 1 Geometry (51-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)