# zbMATH — the first resource for mathematics

## Numerical Methods for Partial Differential Equations

### An International Journal

 Short Title: Numer. Methods Partial Differ. Equations Publisher: Wiley, Hoboken, NJ ISSN: 0749-159X; 1098-2426/e Online: http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1098-2426/issues
 Documents Indexed: 2,036 Publications (since 1985) References Indexed: 1,785 Publications with 42,302 References.
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#### Latest Issues

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#### Authors

 44 Dehghan Takht Fooladi, Mehdi 26 Sun, Zhizhong 25 Wang, Hong 23 He, Yinnian 20 Herrera, Ismael 19 Mohanty, Ranjan Kumar 17 Chen, Zhangxin 17 Mickens, Ronald Elbert 16 Hayat, Tasawar 15 Dai, Weizhong 15 Ewing, Richard Edward 14 Ganji, Davood Domiri 14 Rui, Hongxing 13 Whiteman, John Robert 12 Khaliq, Abdul Q. M. 12 Layton, William J. 12 Li, Jian 12 Ma, Yichen 12 Zhang, Zhimin 11 Allen, Myron Bartlett III 11 Lin, Yanping 10 Gatica, Gabriel N. 10 Hromadka, Theodore V. II 10 Omrani, Khaled 10 Pinder, George Francis 10 Sezer, Mehmet 10 Stephan, Ernst Peter 10 Wang, Kaixin 10 Ye, Xiu 10 Yuan, Yirang 9 Al-Lawatia, Mohamed 9 Babuška, Ivo 9 Cooke, Charlie H. 9 Heuer, Norbert 9 Hou, Yanren 9 Li, Jichun 9 Pani, Amiya Kumar 8 Carey, Graham Francis 8 Celia, Michael A. 8 Ervin, Vincent J. 8 Lin, Tao 8 Power, Henry 8 Zhang, Jun 8 Zhu, Qiding 7 Bürger, Raimund 7 Cheng, Aijie 7 Chou, So-Hsiang 7 Feng, Xinlong 7 Huang, Yunqing 7 Li, Kaitai 7 Ma, Heping 7 Mattheij, Robert M. M. 7 Oden, John Tinsley 7 Rebholz, Leo G. 7 Sheen, Dongwoo 7 Sheng, Qin 7 Whitley, Robert J. 7 Yang, Danping 6 Biazar, Jafar 6 Bruch, John C. jun. 6 Cai, Zhiqiang 6 Chen, Wen 6 Dağ, İdris 6 Eymard, Robert 6 Farhloul, Mohamed 6 Gülsu, Mustafa 6 Karageorghis, Andreas 6 Kwak, Do Young 6 Lazarov, Raytcho D. 6 Mai-Duy, Nam 6 Mei, Liquan 6 Nassar, Raja F. 6 Pao, Chia-Ven 6 Park, Eun-Jae 6 Rivière, Beatrice M. 6 Shi, Dongyang 6 Tran-Cong, Thanh 6 Twizell, E. H. 6 Vong, Seakweng 6 Wu, Li 6 Yates, Robert A. 6 Zhang, Luming 5 Achouri, Talha 5 Beirão da Veiga, Lourenço 5 Bi, Chunjia 5 Bialecki, Bernard 5 Bowers, Kenneth L. 5 Chen, Ching-Shyang 5 Chen, Yanping 5 Deng, Weihua 5 He, Wenming 5 Hu, Xiuling 5 Jafari, Hossein 5 Kim, Sangdong 5 Lesnic, Daniel 5 Li, Qian 5 Li, Xiaoli 5 Li, Zi-Cai 5 Liang, Dong 5 Liu, Jinghong ...and 2,478 more Authors
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#### Fields

 1,771 Numerical analysis (65-XX) 1,267 Partial differential equations (35-XX) 535 Fluid mechanics (76-XX) 146 Mechanics of deformable solids (74-XX) 65 Ordinary differential equations (34-XX) 57 Biology and other natural sciences (92-XX) 56 Classical thermodynamics, heat transfer (80-XX) 54 Integral equations (45-XX) 52 Optics, electromagnetic theory (78-XX) 40 Calculus of variations and optimal control; optimization (49-XX) 40 Geophysics (86-XX) 27 Statistical mechanics, structure of matter (82-XX) 24 Probability theory and stochastic processes (60-XX) 19 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 13 Potential theory (31-XX) 10 Approximations and expansions (41-XX) 9 Dynamical systems and ergodic theory (37-XX) 8 Real functions (26-XX) 8 Functional analysis (46-XX) 7 Operator theory (47-XX) 7 Computer science (68-XX) 6 Integral transforms, operational calculus (44-XX) 6 Quantum theory (81-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Special functions (33-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Astronomy and astrophysics (85-XX) 3 Operations research, mathematical programming (90-XX) 2 General and overarching topics; collections (00-XX) 2 Difference and functional equations (39-XX) 1 History and biography (01-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Mechanics of particles and systems (70-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX)

#### Citations contained in zbMATH Open

1,738 Publications have been cited 16,429 times in 11,098 Documents Cited by Year
Variational formulation for the stationary fractional advection dispersion equation. Zbl 1095.65118
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2006
Simple nonconforming quadrilateral Stokes element. Zbl 0742.76051
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$$H$$-$$p$$ clouds – an $$h$$-$$p$$ meshless method. Zbl 0869.65069
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1996
Solving nonlinear fractional partial differential equations using the homotopy analysis method. Zbl 1185.65187
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2010
Exponential convergence and $$h$$-$$c$$ multiquadric collocation method for partial differential equations. Zbl 1031.65121
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2003
Discontinuous Galerkin approximations for elliptic problems. Zbl 0957.65099
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2000
Variational solution of fractional advection dispersion equations on bounded domains in $$\mathbb R^{d}$$. Zbl 1117.65169
Ervin, Vincent J.; Roop, John Paul
2007
On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Zbl 1059.65072
Dehghan, Mehdi
2005
Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Zbl 1058.76046
Kurganov, Alexander; Tadmor, Eitan
2002
A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions. Zbl 1208.65164
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2011
Contributions to the mathematics of the nonstandard finite difference method and applications. Zbl 0988.65055
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2001
Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations. Zbl 1196.65154
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2010
Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes. Zbl 1314.65151
Mu, Lin; Wang, Junping; Ye, Xiu
2014
An immersed finite element space and its approximation capability. Zbl 1057.65085
Li, Z.; Lin, T.; Lin, Y.; Rogers, R. C.
2004
A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Zbl 1084.65099
Dehghan, Mehdi
2006
The method of approximate particular solutions for solving certain partial differential equations. Zbl 1242.65267
Chen, C. S.; Fan, C. M.; Wen, P. H.
2012
A numerical method for solving the hyperbolic telegraph equation. Zbl 1145.65078
Dehghan, Mehdi; Shokri, Ali
2008
A decoupling method with different subdomain time steps for the nonstationary Stokes-Darcy model. Zbl 1364.76096
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2013
A high-order compact formulation for the 3D Poisson equation. Zbl 0866.65066
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1996
Finite volume element approximations of nonlocal reactive flows in porous media. Zbl 0961.76050
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2000
Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. Zbl 1067.65092
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2004
Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method. Zbl 1186.65136
Saadatmandi, Abbas; Dehghan, Mehdi
2010
Approximation capability of a bilinear immersed finite element space. Zbl 1154.65090
He, Xiaoming; Lin, Tao; Lin, Yanping
2008
ODE solvers and the method of lines. Zbl 0826.65082
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1994
A compact multipoint flux approximation method with improved robustness. Zbl 1230.65114
Aavatsmark, I.; Eigestad, G. T.; Mallison, B. T.; Nordbotten, J. M.
2008
Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Zbl 1111.65101
Andreianov, Boris; Boyer, Franck; Hubert, Florence
2007
Extension of high-order compact schemes to time-dependent problems. Zbl 0998.65101
Spotz, W. F.; Carey, G. F.
2001
Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement. Zbl 1069.65104
Dehghan, Mehdi
2005
An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation. Zbl 0990.65101
Mohanty, R. K.; Jain, M. K.
2001
On the relationship between finite volume and finite element methods applied to the Stokes equations. Zbl 1017.76057
Ye, Xiu
2001
Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094
Mickens, Ronald E.
2007
Unified finite element discretizations of coupled Darcy-Stokes flow. Zbl 1157.76026
Karper, Trygve; Mardal, Kent-Andre; Winther, Ragnar
2009
Efficient numerical methods for pricing American options under stochastic volatility. Zbl 1152.91516
Ikonen, Samuli; Toivanen, Jari
2008
A multilevel finite element method in space-time for the Navier-Stokes problem. Zbl 1081.76044
He, Yinnian; Liu, Kam-Moon
2005
Numerical analysis and computational testing of a high accuracy Leray-deconvolution model of turbulence. Zbl 1191.76061
Layton, William; Manica, Carolina C.; Neda, Monika; Rebholz, Leo G.
2008
High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation. Zbl 1156.65087
Dehghan, Mehdi; Mohebbi, Akbar
2009
Finite volume methods on Voronoi meshes. Zbl 0903.65083
Mishev, Ilya D.
1998
Domain decomposition for radial basis meshless methods. Zbl 1048.65124
Li, Jichun; Hon, Y. C.
2004
Trefftz, collocation, and other boundary methods – a comparison. Zbl 1223.65093
Li, Zi-Cai; Lu, Tzon-Tzer; Huang, Hung-Tsai; Cheng, Alexander H.-D.
2007
Some remarks on Zienkiewicz-Zhu estimator. Zbl 0806.73069
Rodríguez, Rodolfo
1994
Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. Zbl 1077.76037
Burman, Erik; Hansbo, Peter
2005
Compact difference schemes for heat equation with Neumann boundary conditions. Zbl 1181.65115
Sun, Zhi-Zhong
2009
An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes model. Zbl 1364.76091
Minjeaud, Sebastian
2013
Polynomial particular solutions for certain partial differential operators. Zbl 1019.65096
Golberg, M. A.; Muleshkov, A. S.; Chen, C. S.; Cheng, A. H.-D.
2003
Error estimates for finite volume element methods for general second-order elliptic problems. Zbl 1040.65091
Wu, Haijun; Li, Ronghua
2003
Exact solutions to a finite-difference model of a nonlinear reaction- advection equation: Implications for numerical analysis. Zbl 0693.65059
Mickens, Ronald E.
1989
A two-grid stabilization method for solving the steady-state Navier-Stokes equations. Zbl 1089.76034
Kaya, Songul; Rivière, Béatrice
2006
Numerical solutions of some parabolic inverse problems. Zbl 0709.65105
Cannon, John R.; Yin, Hong-Ming
1990
Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace’s, Poisson’s, and the elasticity equations. Zbl 0854.65089
Babuška, Ivo; Strouboulis, T.; Upadhyay, C. S.; Gangaraj, S. K.
1996
A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086
Mickens, Ronald E.; Jordan, P. M.
2004
An analysis of the finite element method for natural convection problems. Zbl 0703.76071
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1990
Virtual element methods for parabolic problems on polygonal meshes. Zbl 1336.65171
Vacca, Giuseppe; Beirão da Veiga, Lourenco
2015
An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Zbl 0822.65085
Herbin, Raphaèle
1995
A meshless method for numerical solution of a linear hyperbolic equation with variable coefficients in two space dimensions. Zbl 1159.65084
Dehghan, Mehdi; Shokri, Ali
2009
Numerical solution of parametrized Navier-Stokes equations by reduced basis methods. Zbl 1178.76238
Quarteroni, Alfio; Rozza, Gianluigi
2007
$$L^p$$ error estimates and superconvergence for covolume or finite volume element methods. Zbl 1029.65123
Chou, So-Hsiang; Kwak, Do Y.; Li, Qian
2003
On the convergence of the multi-point flux approximation O-method: numerical experiments for discontinuous permeability. Zbl 1089.76037
Eigestad, G. T.; Klausen, R. A.
2005
Trefftz method: A general theory. Zbl 0978.65114
Herrera, Ismael
2000
The use of Chebyshev cardinal functions for solution of the second-order one-dimensional telegraph equation. Zbl 1169.65102
Dehghan, Mehdi; Lakestani, Mehrdad
2009
High-order difference schemes for two-dimensional elliptic equations. Zbl 0634.65078
Gupta, Murli M.; Manohar, Ram P.; Stephenson, John W.
1985
High order compact solution of the one-space-dimensional linear hyperbolic equation. Zbl 1151.65071
Mohebbi, Akbar; Dehghan, Mehdi
2008
Weak Galerkin finite element methods for parabolic equations. Zbl 1307.65133
Li, Qiaoluan H.; Wang, Junping
2013
Immersed finite element methods for parabolic equations with moving interface. Zbl 1266.65165
He, Xiaoming; Lin, Tao; Lin, Yanping; Zhang, Xu
2013
A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions. Zbl 1135.65380
Dehghan, M.; Shokri, Ali
2008
Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws. Zbl 1071.65122
Kurganov, Alexander; Petrova, Guergana
2005
Numerical methods for structured population models: The escalator boxcar train. Zbl 0658.92016
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1988
Convergence analysis of a new mixed finite element method for Biot’s consolidation model. Zbl 1350.74024
Yi, Son-Young
2014
Finite difference discretization of the Benjamin-Bona-Mahony-Burgers equation. Zbl 1133.65067
Omrani, Khaled; Ayadi, Mekki
2008
Mixed finite element methods for generalized Forchheimer flow in porous media. Zbl 1141.76425
Park, Eun-Jae
2005
Condition number estimates for combined potential integral operators in acoustics and their boundary element discretisation. Zbl 1272.76217
Betcke, T.; Chandler-Wilde, S. N.; Graham, I. G.; Langdon, S.; Lindner, M.
2011
Convergence of multipoint flux approximations on quadrilateral grids. Zbl 1106.76043
Klausen, Runhild A.; Winther, Ragnar
2006
A second-order splitting combined with orthogonal cubic spline collocation method for the Rosenau equation. Zbl 0930.65111
Manickam, S. Arul Veda; Pani, Amiya K.; Chung, Sang K.
1998
The numerical solution of the second Painlevé equation. Zbl 1172.65037
Dehghan, Mehdi; Shakeri, Fatemeh
2009
Determination of a control function in three-dimensional parabolic equations by Legendre pseudospectral method. Zbl 1252.65161
Shamsi, M.; Dehghan, Mehdi
2012
A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media. Zbl 1008.76044
Yang, Danping
2001
An efficient high-order algorithm for solving systems of reaction-diffusion equations. Zbl 0997.65105
Liao, Wenyuan; Zhu, Jianping; Khaliq, Abdul Q. M.
2002
Numerical solution of the one-dimensional wave equation with an integral condition. Zbl 1112.65097
Saadatmandi, Abbas; Dehghan, Mehdi
2007
Variational multiscale proper orthogonal decomposition: Navier-Stokes equations. Zbl 1452.76048
Iliescu, Traian; Wang, Zhu
2014
A Jacobi spectral Galerkin method for the integrated forms of fourth-order elliptic differential equations. Zbl 1170.65099
Doha, Eid H.; Bhrawy, Ali H.
2009
Modified methods of fundamental solutions for harmonic and biharmonic problems with boundary singularities. Zbl 0760.65103
Karageorghis, Andreas
1992
A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations. Zbl 0852.76039
Ervin, V.; Layton, W.; Maubach, J.
1996
Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085
Mickens, Ronald E.
1999
A two-grid method for mixed finite-element solution of reaction-diffusion equations. Zbl 0929.65079
Wu, Li; Allen, Myron B. III
1999
The h-p version of the finite element method for parabolic equations. I: The p-version in time. Zbl 0693.65078
Babuška, Ivo; Janik, Tadeusz
1989
The p-version of the finite element method for domains with corners and for infinite domains. Zbl 0717.65084
Babuška, Ivo; Oh, Hae-Soo
1990
A finite difference scheme for solving the heat transport equation at the microscale. Zbl 0945.65096
Dai, Weizhong; Nassar, Raja
1999
Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem. Zbl 1048.65102
Buckmire, Ron
2004
The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation. Zbl 1153.65099
Dehghan, Mehdi; Mirzaei, Davoud
2008
Investigations of nonstandard, Mickens-type, finite difference schemes for singular boundary value problems in cylindrical or spherical coordinates. Zbl 1079.76048
Buckmire, Ron
2003
On the convergence of a combined finite volume-finite element method for nonlinear convection-diffusion problems. Zbl 0869.65057
Feistauer, Miloslav; Felcman, Jiří; Lukáčová-Medvid’ová, Mária
1997
Symbolic derivation of finite difference approximations for the three-dimensional Poisson equation. Zbl 0926.65103
Gupta, Murli M.; Kouatchou, Jules
1998
The convergence of the bilinear and linear immersed finite element solutions to interface problems. Zbl 1241.65090
He, Xiaoming; Lin, Tao; Lin, Yanping
2012
A Fourier pseudospectral method for the “good” Boussinesq equation with second-order temporal accuracy. Zbl 1327.65195
Cheng, Kelong; Feng, Wenqiang; Gottlieb, Sigal; Wang, Cheng
2015
Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem. Zbl 1381.76158
Colmenares, Eligio; Gatica, Gabriel N.; Oyarzúa, Ricardo
2016
A compact finite difference scheme for solving a three-dimensional heat transport equation in a thin film. Zbl 0961.65072
Dai, Weizhong; Nassar, Raja
2000
Variational iteration method for solving the space- and time-fractional KdV Equation. Zbl 1130.65132
Momani, Shaher; Odibat, Zaid; Alawneh, Ahmed
2008
A meshless method using the radial basis functions for numerical solution of the regularized long wave equation. Zbl 1195.65142
Shokri, Ali; Dehghan, Mehdi
2010
Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059
Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo
2010
Fourth-order finite difference methods for three-dimensional general linear elliptic problems with variable coefficients. Zbl 0651.65068
Ananthakrishnaiah, U.; Manohar, R.; Stephenson, J. W.
1987
From the fitting techniques to accurate schemes for the Liouville-Bratu-Gelfand problem. Zbl 1099.65098
Serghini Mounim, A.; de Dormale, B. M.
2006
Fast high order difference schemes for the time fractional telegraph equation. Zbl 1452.65164
Liang, Yuxiang; Yao, Zhongsheng; Wang, Zhibo
2020
A reduced-order extrapolated Crank-Nicolson collocation spectral method based on proper orthogonal decomposition for the two-dimensional viscoelastic wave equations. Zbl 1457.65146
Luo, Zhendong; Jin, Shiju
2020
Convergence and stability estimates in difference setting for time-fractional parabolic equations with functional delay. Zbl 1452.65159
Hendy, Ahmed S.; Pimenov, Vladimir G.; Macías-Díaz, Jorge E.
2020
$$H^1$$-superconvergence of finite difference method based on $$Q_1$$-element on quasi-uniform mesh for the 3D Poisson equation. Zbl 1450.65137
Feng, Xinlong; He, Ruijian; Chen, Zhangxin
2020
A fully conservative block-centered finite difference method for Darcy-Forchheimer incompressible miscible displacement problem. Zbl 1451.76083
Li, Xiaoli; Rui, Hongxing
2020
An efficient difference scheme for the coupled nonlinear fractional Ginzburg-Landau equations with the fractional Laplacian. Zbl 1419.65024
Li, Meng; Huang, Chengming
2019
A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions. Zbl 1415.65237
Rahimkhani, Parisa; Ordokhani, Yadollah
2019
Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes. Zbl 1419.65040
Adak, Dibyendu; Natarajan, E.; Kumar, Sarvesh
2019
A numerical approach for solving weakly singular partial integro-differential equations via two-dimensional-orthonormal Bernstein polynomials with the convergence analysis. Zbl 1418.65145
Mirzaee, Farshid; Alipour, Sahar; Samadyar, Nasrin
2019
Approximation capabilities of immersed finite element spaces for elasticity interface problems. Zbl 1418.65174
Guo, Ruchi; Lin, Tao; Lin, Yanping
2019
Spectral collocation methods for nonlinear weakly singular Volterra integro-differential equations. Zbl 1416.65236
Shi, Xiulian; Wei, Yunxia; Huang, Fenglin
2019
Reconstructing unknown nonlinear boundary conditions in a time-fractional inverse reaction-diffusion-convection problem. Zbl 1418.65120
Babaei, Afshin; Banihashemi, Seddigheh
2019
Uniformly convergent novel finite difference methods for singularly perturbed reaction-diffusion equations. Zbl 1431.65198
He, Xuefei; Wang, Kun
2019
Numerical approximation of the generalized regularized long wave equation using Petrov-Galerkin finite element method. Zbl 1431.65169
Bhowmik, Samir Kumar; Karakoc, Seydi B. G.
2019
Transcendental Bernstein series for solving reaction-diffusion equations with nonlocal boundary conditions through the optimization technique. Zbl 1431.65184
Avazzadeh, Zakieh; Hassani, Hossein
2019
A novel variable-order fractional nonlinear Klein Gordon model: a numerical approach. Zbl 1425.65091
Sweilam, Nasser H.; Al-mekhlafi, Seham M.; Albalawi, Anan O.
2019
Extension of a simplified Baldwin-Lomax model to nonequilibrium turbulence: model, analysis and algorithms. Zbl 1423.76271
Rong, Yao; Layton, William; Zhao, Haiyun
2019
A linear, decoupled fractional time-stepping method for the nonlinear fluid-fluid interaction. Zbl 1423.76253
Li, Jian; Huang, Pengzhan; Zhang, Chong; Guo, Gaihui
2019
Numerical study of a conservative weighted compact difference scheme for the symmetric regularized long wave equations. Zbl 1416.76185
Li, Shuguang
2019
Preconditioning trace coupled $$3d-1d$$ systems using fractional Laplacian. Zbl 1437.65014
Kuchta, Miroslav; Mardal, Kent-Andre; Mortensen, Mikael
2019
Patch-Wise local projection stabilized finite element methods for convection-diffusion-reaction problems. Zbl 1418.65171
Dond, Asha K.; Gudi, Thirupathi
2019
Numerical solution of nonlinear partial quadratic integro-differential equations of fractional order via hybrid of block-pulse and parabolic functions. Zbl 1418.65152
Mirzaee, Farshid; Alipour, Sahar
2019
The method of fundamental solutions for the Oseen steady-state viscous flow past obstacles of known or unknown shapes. Zbl 1430.76390
Karageorghis, Andreas; Lesnic, Daniel
2019
A DGFEM for nondivergence form elliptic equations with cordes coefficients on curved domains. Zbl 1425.65163
Kawecki, Ellya L.
2019
Weak Galerkin finite element methods for a fourth order parabolic equation. Zbl 1425.65107
Chai, Shimin; Zou, Yongkui; Zhou, Chenguang; Zhao, Wenju
2019
Optimal estimates on stabilized finite volume methods for the incompressible Navier-Stokes model in three dimensions. Zbl 1419.65039
Li, Jian; Lin, Xiaolin; Zhao, Xin
2019
On the numerical approximation of $$p$$-biharmonic and $$\infty$$-biharmonic functions. Zbl 1419.65113
Katzourakis, Nikos; Pryer, Tristan
2019
Finite difference schemes for the two-dimensional semilinear wave equation. Zbl 1419.65008
Achouri, Talha
2019
Partitioned penalty methods for the transport equation in the evolutionary Stokes-Darcy-transport problem. Zbl 1419.76437
Ervin, V.; Kubacki, M.; Layton, W.; Moraiti, M.; Si, Z.; Trenchea, C.
2019
Unconditional superconvergent analysis of a new mixed finite element method for Ginzburg-Landau equation. Zbl 1419.65042
Shi, Dongyang; Liu, Qian
2019
Spectrally accurate energy-preserving methods for the numerical solution of the “good” Boussinesq equation. Zbl 1418.65117
Brugnano, Luigi; Gurioli, Gianmarco; Zhang, Chengjian
2019
A boundary element approach for solving plane elastostatic equations of anisotropic functionally graded materials. Zbl 1416.74095
Ang, Whye-Teong
2019
Development of a $${P}_2$$ element with optimal $${L}^2$$ convergence for biharmonic equation. Zbl 1418.65181
Mu, Lin; Ye, Xiu; Zhang, Shangyou
2019
Quasi-Toeplitz splitting iteration methods for unsteady space-fractional diffusion equations. Zbl 1418.65097
Dai, Ping-fei; Wu, Qing-Biao; Zhu, Sheng-Feng
2019
Discontinuous Galerkin method for solving the black-oil problem in porous media. Zbl 1416.76097
Cappanera, Loïc; Rivière, Béatrice
2019
Analytical and numerical solutions of a two-dimensional multi-term time-fractional Oldroyd-B model. Zbl 1418.76039
Zhang, Jinghua; Liu, Fawang; Anh, Vo V.
2019
Maximum norm error analysis of an unconditionally stable semi-implicit scheme for multi-dimensional Allen-Cahn equations. Zbl 1418.65099
He, Dongdong; Pan, Kejia
2019
A Crank-Nicolson collocation spectral method for the two-dimensional viscoelastic wave equation. Zbl 1418.76037
Jin, Shiju; Luo, Zhendong
2019
Superconvergence analysis of finite element method for Poisson-Nernst-Planck equations. Zbl 1418.65137
Shi, Dongyang; Yang, Huaijun
2019
Analysis of the operator splitting scheme for the Cahn-Hilliard equation with a viscosity term. Zbl 1430.35201
Weng, Zhifeng; Zhai, Shuying; Feng, Xinlong
2019
Determination of unknown functions in a mathematical model of ductal carcinoma in situ. Zbl 1430.35231
Garshasbi, Morteza
2019
Fractional Crank-Nicolson-Galerkin finite element scheme for the time-fractional nonlinear diffusion equation. Zbl 1431.65133
Kumar, Dileep; Chaudhary, Sudhakar; Kumar, V. V. K. Srinivas
2019
Superconvergence of the direct discontinuous Galerkin method for a time-fractional initial-boundary value problem. Zbl 1431.65216
Huang, Chaobao; Stynes, Martin
2019
New approach to the Lax-Wendroff modified differential equation for linear and nonlinear advection. Zbl 1431.65138
Winnicki, Ireneusz; Jasinski, Janusz; Pietrek, Slawomir
2019
A numerical method for a nonlinear structured population model with an indefinite growth rate coupled with the environment. Zbl 1431.65129
Ackleh, Azmy S.; Miller, Robert L.
2019
Two grid finite element discretization method for semi-linear hyperbolic integro-differential equations. Zbl 1425.65102
Chen, Luoping; Chen, Yanping; Huang, Yunqing
2019
High-order characteristic-tracking strategy for simulation of a nonlinear advection-diffusion equation. Zbl 1425.65099
Bak, Soyoon
2019
New a priori analysis of first-order system least-squares finite element methods for parabolic problems. Zbl 1425.65097
Führer, Thomas; Karkulik, Michael
2019
Numerical scheme for solving system of fractional partial differential equations with Volterra-type integral term through two-dimensional block-pulse functions. Zbl 1425.65214
Xie, Jiaquan; Ren, Zhongkai; Li, Yugui; Wang, Xiaogang; Wang, Tao
2019
Decoupled characteristic stabilized finite element method for time-dependent Navier-Stokes/Darcy model. Zbl 1419.65064
Jia, Xiaofeng; Li, Jichun; Jia, Hongen
2019
A fast second-order difference scheme for the space-time fractional equation. Zbl 1418.65109
Xu, Weiyan; Sun, Hong
2019
A second-order finite difference method for fractional diffusion equation with Dirichlet and fractional boundary conditions. Zbl 1416.65285
Xie, Changping; Fang, Shaomei
2019
Time evolution of discrete fourth-order elliptic operators. Zbl 1418.65096
Ben-Artzi, Matania; Croisille, Jean-Pierre; Fishelov, Dalia
2019
Energy conservation and super convergence analysis of the EC-S-FDTD schemes for Maxwell equations with periodic boundaries. Zbl 1416.78033
Gao, Liping; Cao, Minmin; Shi, Rengang; Guo, Hui
2019
High-order local discontinuous Galerkin method for a fractal mobile/immobile transport equation with the Caputo-Fabrizio fractional derivative. Zbl 1416.82040
Zhang, Min; Liu, Yang; Li, Hong
2019
Finite-volume scheme for a degenerate cross-diffusion model motivated from ion transport. Zbl 1418.65157
Cancès, Clément; Chainais-Hillairet, Claire; Gerstenmayer, Anita; Jüngel, Ansgar
2019
A variable nonlinear splitting algorithm for reaction diffusion systems with self- and cross- diffusion. Zbl 1418.65095
Beauregard, Matthew A.; Padgett, Joshua L.
2019
A finite element approach for analysis and computational modelling of coupled reaction diffusion models. Zbl 1418.65138
Yadav, Om Prakash; Jiwari, Ram
2019
Local and parallel finite element method for solving the biharmonic eigenvalue problem of plate vibration. Zbl 1416.74093
Zhao, Ruilin; Yang, Yidu; Bi, Hai
2019
An analysis of the Robert-Asselin time filter for the correction of nonphysical acoustics in an artificial compression method. Zbl 1418.76031
Decaria, Victor; Layton, William; Mclaughlin, Michael
2019
A fully discrete spectral method for fractional Cattaneo equation based on Caputo-Fabrizo derivative. Zbl 1418.65104
Li, Haonan; Lü, Shujuan; Xu, Tao
2019
Energy stable numerical scheme for the viscous Cahn-Hilliard-Navier-Stokes equations with moving contact line. Zbl 1418.65124
Cherfils, Laurence; Petcu, Madalina
2019
Numerical scheme with convergence for a generalized time-fractional telegraph-type equation. Zbl 1418.65102
Kumar, Kamlesh; Pandey, Rajesh K.; Sharma, Shiva; Xu, Yufeng
2019
Adaptive operator splitting finite element method for Allen-Cahn equation. Zbl 1418.65132
Huang, Yunqing; Yang, Wei; Wang, Hao; Cui, Jintao
2019
The local ultraconvergence of high-order finite element method for second-order elliptic problems with constant coefficients over a rectangular partition. Zbl 1431.65215
He, Wen-ming
2019
Fundamental solutions and asymptotic numerical methods for bifurcation analysis of nonlinear bi-harmonic problems. Zbl 1431.65232
Tri, Abdeljalil; Askour, Omar; Braikat, Bouazza; Zahrouni, Hamid; Potier-ferry, Michel
2019
A correction method for finding lower bounds of eigenvalues of the second-order elliptic and Stokes operators. Zbl 1431.65210
Zhang, Yu; Yang, Yidu
2019
A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer. Zbl 1431.65136
Munyakazi, Justin B.; Patidar, Kailash C.; Sayi, Mbani T.
2019
An upwind center difference parallel method and numerical analysis for the displacement problem with moving boundary. Zbl 1423.76314
Li, Changfeng; Yuan, Yirang
2019
A steady barycentric Lagrange interpolation method for the 2D higher-order time-fractional telegraph equation with nonlocal boundary condition with error analysis. Zbl 1425.65126
Yi, Shi-Chao; Yao, Lin-Quan
2019
On entropy stable schemes for degenerate parabolic multispecies kinematic flow models. Zbl 1425.65085
Bürger, Raimund; Méndez, Paul E.; Parés, Carlos
2019
Least-square collocation and Lagrange multipliers for Taylor meshless method. Zbl 1419.65134
Yang, Jie; Hu, Heng; Potier-Ferry, Michel
2019
A mixed $$hp$$ FEM for the approximation of fourth-order singularly perturbed problems on smooth domains. Zbl 1462.65182
Constantinou, P.; Franz, S.; Ludwig, L.; Xenophontos, C.
2019
Analysis of the immersed boundary method for a finite element Stokes problem. Zbl 1419.65121
Saito, Norikazu; Sugitani, Yoshiki
2019
An adaptive finite element method for a time-dependent Stokes problem. Zbl 1419.65072
Torres, Ricardo Prato; Domínguez, Catalina; Díaz, Stiven
2019
Conservative finite difference methods for fractional Schrödinger-Boussinesq equations and convergence analysis. Zbl 1418.65103
Liao, Feng; Zhang, Luming; Hu, Xiuling
2019
Stabilized multiphysics finite element method with Crank-Nicolson scheme for a poroelasticity model. Zbl 1418.65127
Ge, Zhihao; He, Yanan; Li, Tingting
2019
Numerical error analysis for nonsymmetric interior penalty discontinuous Galerkin method of Cahn-Hilliard equation. Zbl 1418.65134
Liu, Chen; Frank, Florian; Rivière, Béatrice M.
2019
High-order asymptotic-preserving schemes for linear systems: application to the Goldstein-Taylor equations. Zbl 1418.65112
Chalons, Christophe; Turpault, Rodolphe
2019
Operator splitting for numerical solution of the modified Burgers’ equation using finite element method. Zbl 1418.65148
Uçar, Yusuf; Yağmurlu, Nuri M.; Çelikkaya, İhsan
2019
A study on a second order finite difference scheme for fractional advection-diffusion equations. Zbl 1418.65107
Vong, Seakweng; Shi, Chenyang; Lyu, Pin
2019
Stability and convergence of the mark and cell finite difference scheme for Darcy-Stokes-Brinkman equations on non-uniform grids. Zbl 1416.76191
Sun, Yue; Rui, Hongxing
2019
Vorticity-Pressure formulations for the Brinkman-Darcy coupled problem. Zbl 1416.76092
Anaya, Verónica; Mora, David; Reales, Carlos; Ruiz-Baier, Ricardo
2019
An $${h}$$-$${p}$$ version of the Chebyshev spectral collocation method for nonlinear delay differential equations. Zbl 1416.65179
Meng, Tingting; Wang, Zhongqing; Yi, Lijun
2019
A numerical study of the semi-classical limit for three-coupled long wave-short wave interaction equations. Zbl 1418.76040
Oruc, Goksu; Kesici, Emine; Muslu, Gulcin M.
2019
Conservative compact finite difference scheme for the $$N$$-coupled nonlinear Klein-Gordon equations. Zbl 1418.65100
Ji, Bingquan; Zhang, Luming; Zhou, Xuanxuan
2019
A numerical scheme for a kinetic model for mixtures in the diffusive limit using the moment method. Zbl 1418.65119
Bondesan, Andrea; Boudin, Laurent; Grec, Bérénice
2019
Adaptive finite element solution of the porous medium equation in pressure formulation. Zbl 1418.65135
Ngo, Cuong; Huang, Weizhang
2019
Ill-conditioning in the virtual element method: stabilizations and bases. Zbl 1407.65294
Mascotto, Lorenzo
2018
Numerical algorithm for solving time-fractional partial integrodifferential equations subject to initial and Dirichlet boundary conditions. Zbl 1407.65239
Arqub, Omar Abu; Al-Smadi, Mohammed
2018
Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Zbl 1417.65113
Atangana, Abdon; Gómez-aguilar, J. F.
2018
Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space. Zbl 1407.65153
Arqub, Omar Abu
2018
A second-order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection. Zbl 1407.76095
Feng, Wenqiang; Wang, Cheng; Wise, Steven M.; Zhang, Zhengru
2018
Spectral technique for solving variable-order fractional Volterra integro-differential equations. Zbl 1407.65211
Doha, E. H.; Abdelkawy, M. A.; Amin, A. Z. M.; Baleanu, D.
2018
Mathematical analysis and numerical simulation of chaotic noninteger order differential systems with Riemann-Liouville derivative. Zbl 1390.65046
2018
Stability of a finite volume element method for the time-fractional advection-diffusion equation. Zbl 1407.65138
Badr, M.; Yazdani, A.; Jafari, H.
2018
Existence of solution of a finite volume scheme preserving maximum principle for diffusion equations. Zbl 1384.65078
Yuan, Guangwei; Yu, Yunlong
2018
A local radial basis function collocation method to solve the variable-order time fractional diffusion equation in a two-dimensional irregular domain. Zbl 1407.65231
Wei, Song; Chen, Wen; Zhang, Yong; Wei, Hui; Garrard, Rhiannon M.
2018
A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay. Zbl 1407.65176
Singh, Joginder; Kumar, Sunil; Kumar, Mukesh
2018
New conservative difference schemes with fourth-order accuracy for some model equation for nonlinear dispersive waves. Zbl 1390.65068
Ghiloufi, Ahlem; Omrani, Khaled
2018
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#### Cited by 10,935 Authors

 252 Dehghan Takht Fooladi, Mehdi 86 He, Yinnian 80 Shi, Dongyang 71 Wang, Hong 69 Gatica, Gabriel N. 69 Mohanty, Ranjan Kumar 65 Huang, Yunqing 57 Zhang, Zhimin 55 Sun, Zhizhong 52 Abbaszadeh, Mostafa 51 Chen, Zhangxin 51 Li, Jichun 48 Feng, Xinlong 47 Hou, Yanren 47 Rebholz, Leo G. 46 Chen, Yanping 45 Li, Jian 44 Li, Hong 44 Macías-Díaz, Jorge Eduardo 44 Rui, Hongxing 42 Băleanu, Dumitru I. 42 Li, Zi-Cai 41 Liu, Fawang 40 Ruiz-Baier, Ricardo 39 Ye, Xiu 38 Bhrawy, Ali Hassan 37 Chen, Ching-Shyang 36 Demkowicz, Leszek F. 35 Heuer, Norbert 35 Khaliq, Abdul Q. M. 35 Zhang, Jun 34 Bürger, Raimund 34 Lin, Tao 34 Liu, Yang 34 Xu, Da 33 Dai, Weizhong 33 Huang, Pengzhan 33 Zhang, Zhiyue 32 Mohebbi, Akbar 31 Babuška, Ivo 31 He, Xiaoming 31 Karageorghis, Andreas 31 Liu, Chein-Shan 31 Oyarzúa, Ricardo 31 Quarteroni, Alfio M. 31 Wang, Cheng 31 Yıldırım, Ahmet 31 Yuan, Guangwei 30 Wang, Yuanming 30 Yang, Xiaofeng 29 Layton, William J. 29 Li, Xiaolin 29 Mei, Liquan 29 Zhang, Shangyou 28 Führer, Thomas 28 Rozza, Gianluigi 27 Lubuma, Jean Mbaro-Saman 27 Mu, Lin 27 Omrani, Khaled 26 Carstensen, Carsten 25 Doha, Eid H. 25 Fu, Hongfei 25 Li, Xiaoli 25 Sun, Weiwei 24 Huang, Hung-Tsai 24 Lin, Ji 24 Lin, Yanping 24 Mickens, Ronald Elbert 24 Yang, Danping 24 Zhang, Luming 23 Di Pietro, Daniele Antonio 23 Herbin, Raphaèle 23 John, Volker 23 Lakestani, Mehrdad 23 Nicaise, Serge 23 Pani, Amiya Kumar 23 Turner, Ian William 22 Chen, Chuanjun 22 Manafian Heris, Jalil 22 Parand, Kourosh 22 Sezer, Mehmet 22 Shang, Yueqiang 22 Yüzbaşı, Şuayip 22 Zheng, Haibiao 21 Abbasbandy, Saeid 21 Antonietti, Paola Francesca 21 Kurganov, Alexander 21 Kwak, Do Young 21 Li, Zhilin 21 Luo, Zhendong 21 Praetorius, Dirk 21 Saadatmandi, Abbas 21 Sheen, Dongwoo 21 Wang, Tingchun 21 Xu, Jinchao 21 Zheng, Xiangcheng 20 Baccouch, Mahboub 20 Bi, Chunjia 20 Chen, Shaochun 20 Chen, Wenbin ...and 10,835 more Authors
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 716 Computers & Mathematics with Applications 712 Journal of Computational and Applied Mathematics 696 Applied Mathematics and Computation 576 Computer Methods in Applied Mechanics and Engineering 557 Journal of Computational Physics 517 Applied Numerical Mathematics 471 Numerical Methods for Partial Differential Equations 456 Journal of Scientific Computing 362 Engineering Analysis with Boundary Elements 198 International Journal of Computer Mathematics 185 Numerische Mathematik 176 Applied Mathematical Modelling 169 Mathematics of Computation 158 Numerical Algorithms 147 SIAM Journal on Numerical Analysis 132 Mathematics and Computers in Simulation 126 International Journal for Numerical Methods in Engineering 123 Advances in Computational Mathematics 119 Journal of Mathematical Analysis and Applications 114 Mathematical Methods in the Applied Sciences 114 Computational and Applied Mathematics 112 SIAM Journal on Scientific Computing 109 Computers and Fluids 103 Applied Mathematics Letters 98 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 95 Mathematical Problems in Engineering 94 Advances in Applied Mathematics and Mechanics 83 Abstract and Applied Analysis 83 Advances in Difference Equations 78 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 76 Computational Mechanics 73 International Journal for Numerical Methods in Fluids 71 Communications in Nonlinear Science and Numerical Simulation 67 Calcolo 62 Journal of Applied Mathematics and Computing 59 Computer Physics Communications 56 Communications in Computational Physics 55 Journal of Difference Equations and Applications 53 Computational Geosciences 53 Computational Methods in Applied Mathematics 53 International Journal of Applied and Computational Mathematics 52 Applicable Analysis 49 Mathematical and Computer Modelling 48 BIT 48 International Journal of Computational Methods 47 International Journal of Numerical Methods for Heat & Fluid Flow 44 Chaos, Solitons and Fractals 43 Numerical Functional Analysis and Optimization 40 Applications of Mathematics 37 Communications in Numerical Methods in Engineering 37 Discrete and Continuous Dynamical Systems. Series B 35 Journal of Function Spaces 34 Advances in Mathematical Physics 33 Boundary Value Problems 33 Inverse Problems in Science and Engineering 31 Journal of Applied Mathematics 31 Science China. Mathematics 30 Discrete Dynamics in Nature and Society 30 Journal of Numerical Mathematics 29 Applied Mathematics and Mechanics. (English Edition) 29 East Asian Journal on Applied Mathematics 28 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 27 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 25 Computing 23 Nonlinear Dynamics 22 Fractional Calculus & Applied Analysis 20 Journal of Mathematical Chemistry 20 Electronic Research Archive 19 Acta Mathematicae Applicatae Sinica. English Series 19 Comptes Rendus. Mathématique. Académie des Sciences, Paris 19 International Journal of Numerical Analysis and Modeling 18 Numerical Linear Algebra with Applications 18 International Journal of Differential Equations 17 Acta Mechanica 17 Wave Motion 17 Differential Equations and Dynamical Systems 17 Mediterranean Journal of Mathematics 17 Advances in Numerical Analysis 17 International Journal for Numerical Methods in Biomedical Engineering 17 Computational Methods for Differential Equations 16 Journal of Fluid Mechanics 16 Journal of Mathematical Physics 16 Nonlinear Analysis. Real World Applications 16 Journal of Nonlinear Science and Applications 16 Journal of Applied Analysis and Computation 16 Mathematical Sciences 15 Journal of Differential Equations 15 Engineering Computations 15 Communications on Applied Mathematics and Computation 14 Inverse Problems 14 Physica D 14 Archives of Computational Methods in Engineering 14 AMM. Applied Mathematics and Mechanics. (English Edition) 13 International Journal of Heat and Mass Transfer 13 International Journal of Nonlinear Sciences and Numerical Simulation 13 Journal of Mathematics 12 Journal of Engineering Mathematics 12 Journal of Optimization Theory and Applications 12 RAIRO. Modélisation Mathématique et Analyse Numérique 12 Complexity ...and 384 more Journals
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#### Cited in 53 Fields

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