Numerical Methods for Partial Differential EquationsAn International Journal Short Title: Numer. Methods Partial Differ. Equations Publisher: Wiley, Hoboken, NJ ISSN: 0749-159X; 1098-2426/e Online: https://onlinelibrary.wiley.com/loi/10982426 Comments: Journal Documents Indexed: 2,612 Publications (since 1985) References Indexed: 2,359 Publications with 64,033 References. all top 5 Latest Issues 40, No. 1 (2024) 39, No. 6 (2023) 39, No. 5 (2023) 39, No. 4 (2023) 39, No. 3 (2023) 39, No. 2 (2023) 39, No. 1 (2023) 38, No. 6 (2022) 38, No. 5 (2022) 38, No. 4 (2022) 38, No. 3 (2022) 38, No. 2 (2022) 38, No. 1 (2022) 37, No. 6 (2021) 37, No. 5 (2021) 37, No. 4 (2021) 37, No. 3 (2021) 37, No. 2 (2021) 37, No. 1 (2021) 36, No. 6 (2020) 36, No. 5 (2020) 36, No. 4 (2020) 36, No. 3 (2020) 36, No. 2 (2020) 36, No. 1 (2020) 35, No. 6 (2019) 35, No. 5 (2019) 35, No. 4 (2019) 35, No. 3 (2019) 35, No. 2 (2019) 35, No. 1 (2019) 34, No. 6 (2018) 34, No. 5 (2018) 34, No. 4 (2018) 34, No. 3 (2018) 34, No. 2 (2018) 34, No. 1 (2018) 33, No. 6 (2017) 33, No. 5 (2017) 33, No. 4 (2017) 33, No. 3 (2017) 33, No. 2 (2017) 33, No. 1 (2017) 32, No. 6 (2016) 32, No. 5 (2016) 32, No. 4 (2016) 32, No. 3 (2016) 32, No. 2 (2016) 32, No. 1 (2016) 31, No. 6 (2015) 31, No. 5 (2015) 31, No. 4 (2015) 31, No. 3 (2015) 31, No. 2 (2015) 31, No. 1 (2015) 30, No. 6 (2014) 30, No. 5 (2014) 30, No. 4 (2014) 30, No. 3 (2014) 30, No. 2 (2014) 30, No. 1 (2014) 29, No. 6 (2013) 29, No. 5 (2013) 29, No. 4 (2013) 29, No. 3 (2013) 29, No. 2 (2013) 29, No. 1 (2013) 28, No. 6 (2012) 28, No. 5 (2012) 28, No. 4 (2012) 28, No. 2 (2012) 28, No. 1 (2012) 27, No. 6 (2011) 27, No. 5 (2011) 27, No. 4 (2011) 27, No. 3 (2011) 27, No. 2 (2011) 27, No. 1 (2011) 26, No. 6 (2010) 26, No. 5 (2010) 26, No. 4 (2010) 26, No. 3 (2010) 26, No. 2 (2010) 26, No. 1 (2010) 25, No. 6 (2009) 25, No. 5 (2009) 25, No. 4 (2009) 25, No. 3 (2009) 25, No. 2 (2009) 25, No. 1 (2009) 24, No. 6 (2008) 24, No. 5 (2008) 24, No. 4 (2008) 24, No. 3 (2008) 24, No. 2 (2008) 24, No. 1 (2008) 23, No. 6 (2007) 23, No. 5 (2007) 23, No. 4 (2007) 23, No. 3 (2007) ...and 112 more Volumes all top 5 Authors 51 Dehghan Takht Fooladi, Mehdi 31 Sun, Zhizhong 29 Wang, Hong 25 He, Yinnian 20 Herrera, Ismael 19 Mohanty, Ranjan Kumar 17 Chen, Zhangxin 17 Dai, Weizhong 17 Mickens, Ronald Elbert 16 Hayat, Tasawar 16 Rui, Hongxing 15 Ewing, Richard Edward 14 Khaliq, Abdul Q. M. 14 Layton, William J. 13 Ganji, Davood Domiri 13 Li, Jian 13 Whiteman, John Robert 13 Ye, Xiu 12 Jain, Mahinder Kumar 12 Ma, Yichen 12 Shi, Dongyang 12 Zhang, Zhimin 11 Allen, Myron Bartlett III 11 Gatica, Gabriel N. 11 Hou, Yanren 11 Lin, Yanping 11 Omrani, Khaled 11 Stephan, Ernst Peter 10 Akgül, Ali 10 Hromadka, Theodore V. II 10 Pani, Amiya Kumar 10 Pinder, George Francis 10 Sezer, Mehmet 10 Sooppy Nisar, Kottakkaran 10 Wang, Kaixin 10 Xu, Da 10 Yuan, Yirang 9 Al-Lawatia, Mohamed 9 Babuška, Ivo 9 Cooke, Charlie H. 9 Feng, Xinlong 9 Heuer, Norbert 9 Li, Jichun 9 Rebholz, Leo G. 9 Sheen, Dongwoo 8 Bürger, Raimund 8 Carey, Graham Francis 8 Celia, Michael A. 8 Ervin, Vincent J. 8 Huang, Yunqing 8 Kumar, Sunil 8 Li, Xiaoli 8 Lin, Tao 8 Power, Henry 8 Udhayakumar, Ramalingam 8 Vijayakumar, Velusamy 8 Vong, Seakweng 8 Zhang, Jun 8 Zhang, Shangyou 8 Zhu, Qiding 7 Atangana, Abdon 7 Bochev, Pavel B. 7 Chen, Yanping 7 Cheng, Aijie 7 Chou, So-Hsiang 7 Gómez-Aguilar, José Francisco 7 He, Wenming 7 Lazarov, Raytcho D. 7 Li, Hong 7 Li, Kaitai 7 Ma, Heping 7 Mattheij, Robert M. M. 7 Oden, John Tinsley 7 Park, Eun-Jae 7 Rivière, Beatrice M. 7 Sheng, Qin 7 Whitley, Robert J. 7 Yang, Danping 6 Biazar, Jafar 6 Bruch, John C. jun. 6 Cai, Zhiqiang 6 Chen-Charpentier, Benito Miguel 6 Chen, Wen 6 Chu, Yuming 6 Dağ, İdris 6 Eymard, Robert 6 Farhloul, Mohamed 6 Gao, Zhiming 6 Gülsu, Mustafa 6 Jafari, Hossein 6 Karageorghis, Andreas 6 Kwak, Do Young 6 Mai-Duy, Nam 6 Mei, Liquan 6 Mu, Lin 6 Nassar, Raja F. 6 Nicaise, Serge 6 Pao, Chia-Ven 6 Shang, Yueqiang 6 Skiba, Yuri N. ...and 3,382 more Authors all top 5 Fields 2,323 Numerical analysis (65-XX) 1,790 Partial differential equations (35-XX) 575 Fluid mechanics (76-XX) 155 Mechanics of deformable solids (74-XX) 70 Ordinary differential equations (34-XX) 70 Biology and other natural sciences (92-XX) 64 Classical thermodynamics, heat transfer (80-XX) 58 Integral equations (45-XX) 58 Optics, electromagnetic theory (78-XX) 48 Calculus of variations and optimal control; optimization (49-XX) 42 Real functions (26-XX) 40 Geophysics (86-XX) 33 Probability theory and stochastic processes (60-XX) 30 Statistical mechanics, structure of matter (82-XX) 20 Approximations and expansions (41-XX) 20 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 14 Potential theory (31-XX) 13 Operator theory (47-XX) 12 Computer science (68-XX) 10 Integral transforms, operational calculus (44-XX) 10 Functional analysis (46-XX) 10 Systems theory; control (93-XX) 9 Dynamical systems and ergodic theory (37-XX) 7 Special functions (33-XX) 6 Statistics (62-XX) 6 Quantum theory (81-XX) 5 Combinatorics (05-XX) 5 Linear and multilinear algebra; matrix theory (15-XX) 4 Astronomy and astrophysics (85-XX) 4 Operations research, mathematical programming (90-XX) 3 General and overarching topics; collections (00-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Differential geometry (53-XX) 3 Global analysis, analysis on manifolds (58-XX) 2 Difference and functional equations (39-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Mechanics of particles and systems (70-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 2,034 Publications have been cited 22,438 times in 15,025 Documents Cited by ▼ Year ▼ Variational formulation for the stationary fractional advection dispersion equation. Zbl 1095.65118 Ervin, Vincent J.; Roop, John Paul 433 2006 Simple nonconforming quadrilateral Stokes element. Zbl 0742.76051 Rannacher, R.; Turek, S. 299 1992 Solving nonlinear fractional partial differential equations using the homotopy analysis method. Zbl 1185.65187 Dehghan, Mehdi; Manafian, Jalil; Saadatmandi, Abbas 285 2010 \(H\)-\(p\) clouds – an \(h\)-\(p\) meshless method. Zbl 0869.65069 Duarte, C. Armando; Oden, J. Tinsley 217 1996 Exponential convergence and \(h\)-\(c\) multiquadric collocation method for partial differential equations. Zbl 1031.65121 Cheng, A. H.-D.; Golberg, M. A.; Kansa, E. J.; Zammito, G. 195 2003 Discontinuous Galerkin approximations for elliptic problems. Zbl 0957.65099 Brezzi, F.; Manzini, G.; Marini, D.; Pietra, P.; Russo, A. 170 2000 Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers. Zbl 1058.76046 Kurganov, Alexander; Tadmor, Eitan 168 2002 Variational solution of fractional advection dispersion equations on bounded domains in \(\mathbb R^{d}\). Zbl 1117.65169 Ervin, Vincent J.; Roop, John Paul 159 2007 A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions. Zbl 1208.65164 Demkowicz, L.; Gopalakrishnan, J. 151 2011 Weak Galerkin finite element methods for the biharmonic equation on polytopal meshes. Zbl 1314.65151 Mu, Lin; Wang, Junping; Ye, Xiu 137 2014 On the solution of an initial-boundary value problem that combines Neumann and integral condition for the wave equation. Zbl 1059.65072 Dehghan, Mehdi 125 2005 An immersed finite element space and its approximation capability. Zbl 1057.65085 Li, Z.; Lin, T.; Lin, Y.; Rogers, R. C. 124 2004 Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations. Zbl 1196.65154 Liao, Honglin; Sun, Zhizhong 123 2010 Contributions to the mathematics of the nonstandard finite difference method and applications. Zbl 0988.65055 Anguelov, Roumen; Lubuma, Jean M.-S. 119 2001 Virtual element methods for parabolic problems on polygonal meshes. Zbl 1336.65171 Vacca, Giuseppe; Beirão da Veiga, Lourenco 106 2015 A numerical method for solving the hyperbolic telegraph equation. Zbl 1145.65078 Dehghan, Mehdi; Shokri, Ali 98 2008 A computational study of the one-dimensional parabolic equation subject to nonclassical boundary specifications. Zbl 1084.65099 Dehghan, Mehdi 96 2006 A decoupling method with different subdomain time steps for the nonstationary Stokes-Darcy model. Zbl 1364.76096 Shan, Li; Zheng, Haibiao; Layton, William J. 93 2013 Numerical approximation of Riemann-Liouville definition of fractional derivative: from Riemann-Liouville to Atangana-Baleanu. Zbl 1417.65113 Atangana, Abdon; Gómez-aguilar, J. F. 90 2018 The method of approximate particular solutions for solving certain partial differential equations. Zbl 1242.65267 Chen, C. S.; Fan, C. M.; Wen, P. H. 87 2012 Approximation capability of a bilinear immersed finite element space. Zbl 1154.65090 He, Xiaoming; Lin, Tao; Lin, Yanping 87 2008 Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method. Zbl 1186.65136 Saadatmandi, Abbas; Dehghan, Mehdi 84 2010 Calculation of denominator functions for nonstandard finite difference schemes for differential equations satisfying a positivity condition. Zbl 1114.65094 Mickens, Ronald E. 82 2007 Discrete duality finite volume schemes for Leray-Lions-type elliptic problems on general 2D meshes. Zbl 1111.65101 Andreianov, Boris; Boyer, Franck; Hubert, Florence 77 2007 A high-order compact formulation for the 3D Poisson equation. Zbl 0866.65066 Spotz, W. F.; Carey, G. F. 76 1996 Error estimates for a finite volume element method for parabolic equations in convex polygonal domains. Zbl 1067.65092 Chatzipantelidis, P.; Lazarov, R. D.; Thomée, V. 76 2004 Finite volume element approximations of nonlocal reactive flows in porous media. Zbl 0961.76050 Ewing, Richard; Lazarov, Raytcho; Lin, Yanping 73 2000 A compact multipoint flux approximation method with improved robustness. Zbl 1230.65114 Aavatsmark, I.; Eigestad, G. T.; Mallison, B. T.; Nordbotten, J. M. 70 2008 An unconditionally stable uncoupled scheme for a triphasic Cahn-Hilliard/Navier-Stokes model. Zbl 1364.76091 Minjeaud, Sebastian 68 2013 Weak Galerkin finite element methods for parabolic equations. Zbl 1307.65133 Li, Qiaoluan H.; Wang, Junping 67 2013 On the relationship between finite volume and finite element methods applied to the Stokes equations. Zbl 1017.76057 Ye, Xiu 65 2001 An unconditionally stable alternating direction implicit scheme for the two space dimensional linear hyperbolic equation. Zbl 0990.65101 Mohanty, R. K.; Jain, M. K. 64 2001 Unified finite element discretizations of coupled Darcy-Stokes flow. Zbl 1157.76026 Karper, Trygve; Mardal, Kent-Andre; Winther, Ragnar 64 2009 Variational multiscale proper orthogonal decomposition: Navier-Stokes equations. Zbl 1452.76048 Iliescu, Traian; Wang, Zhu 64 2014 Efficient numerical methods for pricing American options under stochastic volatility. Zbl 1152.91516 Ikonen, Samuli; Toivanen, Jari 62 2008 ODE solvers and the method of lines. Zbl 0826.65082 Shampine, L. F. 61 1994 Ill-conditioning in the virtual element method: stabilizations and bases. Zbl 1407.65294 Mascotto, Lorenzo 61 2018 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. 60 2008 High order implicit collocation method for the solution of two-dimensional linear hyperbolic equation. Zbl 1156.65087 Dehghan, Mehdi; Mohebbi, Akbar 60 2009 Identification of a time-dependent coefficient in a partial differential equation subject to an extra measurement. Zbl 1069.65104 Dehghan, Mehdi 60 2005 Immersed finite element methods for parabolic equations with moving interface. Zbl 1266.65165 He, Xiaoming; Lin, Tao; Lin, Yanping; Zhang, Xu 60 2013 Stabilized Crouzeix-Raviart element for the Darcy-Stokes problem. Zbl 1077.76037 Burman, Erik; Hansbo, Peter 59 2005 Finite difference discretization of the Benjamin-Bona-Mahony-Burgers equation. Zbl 1133.65067 Omrani, Khaled; Ayadi, Mekki 58 2008 Extension of high-order compact schemes to time-dependent problems. Zbl 0998.65101 Spotz, W. F.; Carey, G. F. 57 2001 A multilevel finite element method in space-time for the Navier-Stokes problem. Zbl 1081.76044 He, Yinnian; Liu, Kam-Moon 57 2005 Finite volume methods on Voronoi meshes. Zbl 0903.65083 Mishev, Ilya D. 57 1998 Convergence analysis of a new mixed finite element method for Biot’s consolidation model. Zbl 1350.74024 Yi, Son-Young 57 2014 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 57 2018 An analysis of the finite element method for natural convection problems. Zbl 0703.76071 Boland, J.; Layton, W. 56 1990 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 56 2018 Numerical solution of parametrized Navier-Stokes equations by reduced basis methods. Zbl 1178.76238 Quarteroni, Alfio; Rozza, Gianluigi 55 2007 Exact solutions to a finite-difference model of a nonlinear reaction- advection equation: Implications for numerical analysis. Zbl 0693.65059 Mickens, Ronald E. 55 1989 A numerical method for one-dimensional nonlinear sine-Gordon equation using collocation and radial basis functions. Zbl 1135.65380 Dehghan, M.; Shokri, Ali 54 2008 Compact difference schemes for heat equation with Neumann boundary conditions. Zbl 1181.65115 Sun, Zhi-Zhong 54 2009 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 54 2009 Some remarks on Zienkiewicz-Zhu estimator. Zbl 0806.73069 Rodríguez, Rodolfo 54 1994 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 54 2015 Trefftz, collocation, and other boundary methods – a comparison. Zbl 1223.65093 Li, Zi-Cai; Lu, Tzon-Tzer; Huang, Hung-Tsai; Cheng, Alexander H.-D. 52 2007 Solutions of time-fractional Tricomi and Keldysh equations of Dirichlet functions types in Hilbert space. Zbl 1407.65153 Arqub, Omar Abu 52 2018 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. 51 1996 Domain decomposition for radial basis meshless methods. Zbl 1048.65124 Li, Jichun; Hon, Y. C. 51 2004 Mixed finite element methods for generalized Forchheimer flow in porous media. Zbl 1141.76425 Park, Eun-Jae 51 2005 Error estimates for finite volume element methods for general second-order elliptic problems. Zbl 1040.65091 Wu, Haijun; Li, Ronghua 50 2003 The use of Chebyshev cardinal functions for solution of the second-order one-dimensional telegraph equation. Zbl 1169.65102 Dehghan, Mehdi; Lakestani, Mehrdad 50 2009 Polynomial particular solutions for certain partial differential operators. Zbl 1019.65096 Golberg, M. A.; Muleshkov, A. S.; Chen, C. S.; Cheng, A. H.-D. 49 2003 High-order numerical methods for one-dimensional parabolic singularly perturbed problems with regular layers. Zbl 1073.65079 Clavero, C.; Gracia, J. L.; Jorge, J. C. 49 2005 High order compact solution of the one-space-dimensional linear hyperbolic equation. Zbl 1151.65071 Mohebbi, Akbar; Dehghan, Mehdi 49 2008 A splitting positive definite mixed element method for miscible displacement of compressible flow in porous media. Zbl 1008.76044 Yang, Danping 48 2001 Some temporal second order difference schemes for fractional wave equations. Zbl 1352.65269 Sun, Hong; Sun, Zhi-Zhong; Gao, Guang-Hua 48 2016 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. 47 2011 Determination of a control function in three-dimensional parabolic equations by Legendre pseudospectral method. Zbl 1252.65161 Shamsi, M.; Dehghan, Mehdi 47 2012 A two-grid stabilization method for solving the steady-state Navier-Stokes equations. Zbl 1089.76034 Kaya, Songul; Rivière, Béatrice 47 2006 The convergence of the bilinear and linear immersed finite element solutions to interface problems. Zbl 1241.65090 He, Xiaoming; Lin, Tao; Lin, Yanping 46 2012 \(L^p\) error estimates and superconvergence for covolume or finite volume element methods. Zbl 1029.65123 Chou, So-Hsiang; Kwak, Do Y.; Li, Qian 46 2003 A coupling of nonconforming and mixed finite element methods for Biot’s consolidation model. Zbl 1274.74455 Yi, Son-Young 46 2013 Numerical methods for structured population models: The escalator boxcar train. Zbl 0658.92016 de Roos, A. M. 45 1988 A positivity-preserving nonstandard finite difference scheme for the damped wave equation. Zbl 1062.65086 Mickens, Ronald E.; Jordan, P. M. 45 2004 Central-upwind schemes on triangular grids for hyperbolic systems of conservation laws. Zbl 1071.65122 Kurganov, Alexander; Petrova, Guergana 45 2005 Numerical solutions of some parabolic inverse problems. Zbl 0709.65105 Cannon, John R.; Yin, Hong-Ming 45 1990 Legendre wavelet method for numerical solutions of partial differential equations. Zbl 1186.65152 Liu, Nanshan; Lin, En-Bing 44 2010 A two-grid method for mixed finite-element solution of reaction-diffusion equations. Zbl 0929.65079 Wu, Li; Allen, Myron B. III 44 1999 A meshless method using the radial basis functions for numerical solution of the regularized long wave equation. Zbl 1195.65142 Shokri, Ali; Dehghan, Mehdi 44 2010 High-order difference schemes for two-dimensional elliptic equations. Zbl 0634.65078 Gupta, Murli M.; Manohar, Ram P.; Stephenson, John W. 43 1985 An error estimate for a finite volume scheme for a diffusion-convection problem on a triangular mesh. Zbl 0822.65085 Herbin, Raphaèle 43 1995 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. 43 1998 Application of a Mickens finite-difference scheme to the cylindrical Bratu-Gelfand problem. Zbl 1048.65102 Buckmire, Ron 43 2004 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. 43 2005 Mixed finite element methods for incompressible flow: stationary Stokes equations. Zbl 1267.76059 Cai, Zhiqiang; Tong, Charles; Vassilevski, Panayot S.; Wang, Chunbo 43 2010 Numerical solution of nonlinear Schrödinger equation by using time-space pseudo-spectral method. Zbl 1195.65137 Dehghan, Mehdi; Taleei, Ameneh 43 2010 Analysis of some finite difference schemes for two-dimensional Ginzburg-Landau equation. Zbl 1233.65062 Wang, Tingchun; Guo, Boling 42 2011 Convergence of multipoint flux approximations on quadrilateral grids. Zbl 1106.76043 Klausen, Runhild A.; Winther, Ragnar 42 2006 Analysis of an augmented mixed-primal formulation for the stationary Boussinesq problem. Zbl 1381.76158 Colmenares, Eligio; Gatica, Gabriel N.; Oyarzúa, Ricardo 42 2016 Numerical solution of the one-dimensional wave equation with an integral condition. Zbl 1112.65097 Saadatmandi, Abbas; Dehghan, Mehdi 41 2007 An efficient high-order algorithm for solving systems of reaction-diffusion equations. Zbl 0997.65105 Liao, Wenyuan; Zhu, Jianping; Khaliq, Abdul Q. M. 41 2002 The boundary integral equation approach for numerical solution of the one-dimensional sine-Gordon equation. Zbl 1153.65099 Dehghan, Mehdi; Mirzaei, Davoud 41 2008 Nonstandard finite difference schemes for reaction-diffusion equations. Zbl 0926.65085 Mickens, Ronald E. 40 1999 Numerical analysis of two partitioned methods for uncoupling evolutionary MHD flows. Zbl 1364.76088 Layton, W.; Tran, H.; Trenchea, C. 40 2014 Trefftz method: A general theory. Zbl 0978.65114 Herrera, Ismael 39 2000 A two-grid characteristic finite volume element method for semilinear advection-dominated diffusion equations. Zbl 1274.65252 Chen, Chuanjun; Liu, Wei; Bi, Chunjia 39 2013 The numerical solution of the second Painlevé equation. Zbl 1172.65037 Dehghan, Mehdi; Shakeri, Fatemeh 38 2009 Existence and controllability of nonlocal mixed Volterra-Fredholm type fractional delay integro-differential equations of order \(1 < r < 2\). Zbl 07798400 Kavitha Williams, W.; Vijayakumar, V.; Udhayakumar, R.; Panda, Sumati Kumari; Nisar, Kottakkaran Sooppy 11 2024 Emphasis on unsteady dynamics of bioconvective hybrid nanofluid flow over an upward-downward moving rotating disk. Zbl 07798391 Jayadevamurthy, Punith Gowda Ramanahalli; Rangaswamy, Naveen Kumar; Prasannakumara, Ballajja Chandrappa; Nisar, Kottakkaran Sooppy 5 2024 Results on existence and controllability results for fractional evolution inclusions of order \(1 < r < 2\) with Clarke’s subdifferential type. Zbl 07798396 Mohan Raja, M.; Vijayakumar, V.; Udhayakumar, R.; Nisar, Kottakkaran Sooppy 3 2024 Numerical investigations on COVID-19 model through singular and non-singular fractional operators. Zbl 07798404 Kumar, Sunil; Chauhan, R. P.; Momani, Shaher; Hadid, Samir 3 2024 Mathematical model for spreading of COVID-19 virus with the Mittag-Leffler kernel. Zbl 07798387 Logeswari, Kumararaju; Ravichandran, Chokkalingam; Nisar, Kottakkaran Sooppy 2 2024 A study on fractional predator-prey-pathogen model with Mittag-Leffler kernel-based operators. Zbl 07798394 Ghanbari, Behzad; Kumar, Sunil 2 2024 Integrated neuro-evolution heuristic with sequential quadratic programming for second-order prediction differential models. Zbl 07798397 Sabir, Zulqurnain; Raja, Muhammad Asif Zahoor; Wahab, Hafiz Abdul; Shoaib, Muhammad; Aguilar, J. F. Gómez 2 2024 A numerical study on fractional differential equation with population growth model. Zbl 07798392 Kumar, Sunil; Shaw, Pawan Kumar; Abdel-Aty, Abdel-Haleem; Mahmoud, Emad E. 1 2024 Analytical and numerical techniques for initial-boundary value problems of Kolmogorov-Petrovsky-Piskunov equation. Zbl 07798398 Wongsaijai, Ben; Aydemir, Tuğba; Ak, Turgut; Dhawan, Sharanjeet 1 2024 Heat transfer analysis on MHD flow over a stretchable Riga wall considering entropy generation rate: a numerical study. Zbl 07798399 Shah, Faisal; Khan, Muhammad Ijaz; Chu, Yu-Ming; Kadry, Seifedine 1 2024 Results on approximate controllability of neutral integro-differential stochastic system with state-dependent delay. Zbl 07798401 Dineshkumar, C.; Udhayakumar, R.; Vijayakumar, V.; Nisar, Kottakkaran Sooppy 1 2024 Decatic B-spline collocation scheme for approximate solution of Burgers’ equation. Zbl 07776988 Jena, Saumya R.; Gebremedhin, Guesh S. 4 2023 Approximate controllability results for Sobolev-type delay differential system of fractional order without uniqueness. Zbl 07777364 Vijayakumar, V.; Udhayakumar, R.; Zhou, Yong; Sakthivel, N. 4 2023 A new \(\phi \)-FEM approach for problems with natural boundary conditions. Zbl 07779711 Duprez, Michel; Lleras, Vanessa; Lozinski, Alexei 4 2023 Thermal instability of magnetohydrodynamic couple stress nanofluid in rotating porous medium. Zbl 07769125 Singh, Bhupander; Nisar, Kottakkaran Sooppy 3 2023 Exact solutions of convective-diffusive Cahn-Hilliard equation using extended direct algebraic method. Zbl 07769128 Rehman, Hamood Ur; Ullah, Naeem; Asjad, Muhammad Imran; Akgül, Ali 2 2023 An inverse problem of identifying the time-dependent potential in a fourth-order pseudo-parabolic equation from additional condition. Zbl 07776941 Huntul, Mousa J.; Tamsir, Mohammad; Dhiman, Neeraj 2 2023 On the SAV-DG method for a class of fourth order gradient flows. Zbl 07776958 Liu, Hailiang; Yin, Peimeng 2 2023 Learning parameters of a system of variable order fractional differential equations. Zbl 07776993 Singh, Abhishek Kumar; Mehra, Mani; Gulyani, Samarth 2 2023 The divergence-free nonconforming virtual element method for the Navier-Stokes problem. Zbl 07776994 Zhang, Bei; Zhao, Jikun; Li, Meng 2 2023 Approximation of functions by a new type of Gamma operators. Zbl 07777366 Betus, Ömür; Usta, Fuat 2 2023 A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters. Zbl 07779730 Bao, Weizhu; Garcke, Harald; Nürnberg, Robert; Zhao, Quan 2 2023 Experimental convergence rate study for three shock-capturing schemes and development of highly accurate combined schemes. Zbl 07769119 Chu, Shaoshuai; Kovyrkina, Olyana A.; Kurganov, Alexander; Ostapenko, Vladimir V. 1 2023 Dynamics of Arrhenius activation energy in flow of Carreau fluid subject to Brownian motion diffusion. Zbl 07769126 Khan, Muhammad Ijaz; Qayyum, Sumaira; Nigar, Mehr; Chu, Yu-Ming; Kadry, Seifedine 1 2023 High-order finite difference/spectral-Galerkin approximations for the nonlinear time-space fractional Ginzburg-Landau equation. Zbl 07769130 Zaky, Mahmoud A.; Hendy, Ahmed S.; Macías-Díaz, Jorge E. 1 2023 Exact solutions of \((2+1)\)-dimensional Schrödinger’s hyperbolic equation using different techniques. Zbl 07769131 Rehman, Hamood Ur; Imran, Muhammad Asjad; Ullah, Naeem; Akgül, Ali 1 2023 Simulation of the interaction of light with 3-D metallic nanostructures using a proper orthogonal decomposition-Galerkin reduced-order discontinuous Galerkin time-domain method. Zbl 07776946 Li, Kun; Huang, Ting-Zhu; Li, Liang; Lanteri, Stéphane 1 2023 Error bounds of fourth-order compact finite difference methods for the Dirac equation in the massless and nonrelativistic regime. Zbl 07776947 Feng, Yue; Ma, Ying 1 2023 Numerical solutions of generalized Rosenau-KDV-RLW equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization. Zbl 07776954 Verma, Amit Kumar; Rawani, Mukesh Kumar 1 2023 A modified walk-on-sphere method for high dimensional fractional Poisson equation. Zbl 07776956 Jiao, Caiyu; Li, Changpin; Wang, Hexiang; Zhang, Zhongqiang 1 2023 A fourth-order accurate numerical method for the distributed-order Riesz space fractional diffusion equation. Zbl 07776962 Chen, Xuejuan; Chen, Jinghua; Liu, Fawang; Sun, Zhi-zhong 1 2023 A fast numerical solution of the nonlinear tempered fractional integrodifferential equation. Zbl 07776965 Qiao, Leijie; Qiu, Wenlin; Tang, Bo 1 2023 Error analysis of a fully discrete projection method for magnetohydrodynamic system. Zbl 07776970 Ding, Qianqian; He, Xiaoming; Long, Xiaonian; Mao, Shipeng 1 2023 A new stable, explicit, and generic third-order method for simulating conductive heat transfer. Zbl 07776972 Kovács, Endre; Nagy, Ádám 1 2023 A novel linearized and momentum-preserving Fourier pseudo-spectral scheme for the Rosenau-Korteweg de Vries equation. Zbl 07776974 Jiang, Chaolong; Cui, Jin; Cai, Wenjun; Wang, Yushun 1 2023 Numerical approximation of the optimal control of a population dynamics model. Zbl 07776975 Alahyane, Mohamed; Soufyane, Abdelaziz; Zahri, Mostafa 1 2023 A novel approach for the solution of fractional diffusion problems with conformable derivative. Zbl 07776989 Bayrak, Mine A.; Demir, Ali; Ozbilge, Ebru 1 2023 Displacement-pseudostress formulation for the linear elasticity spectral problem. Zbl 07776995 Inzunza, Daniel; Lepe, Felipe; Rivera, Gonzalo 1 2023 Linearized compact difference methods for solving nonlinear Sobolev equations with distributed delay. Zbl 07777001 Tan, Zengqiang; Ran, Maohua 1 2023 A \(C^0\) linear finite element method for a second-order elliptic equation in non-divergence form with Cordes coefficients. Zbl 07777005 Xu, Minqiang; Lin, Runchang; Zou, Qingsong 1 2023 A systematic study on weak Galerkin finite element method for second-order parabolic problems. Zbl 07777013 Deka, Bhupen; Kumar, Naresh 1 2023 On two-dimensional weakly singular fractional partial integro-differential equations and dual Bernstein polynomials. Zbl 07777017 Sayevand, Khosro; Mirzaee, Farshid; Masti, Imman 1 2023 A meshfree radial basis function method for simulation of multi-dimensional conservation problems. Zbl 07777020 Foy, Brody H.; Burrage, Kevin; Turner, Ian 1 2023 A kernel-based pseudo-spectral method for multi-term and distributed order time-fractional diffusion equations. Zbl 07777021 Fardi, Mojtaba 1 2023 A kernel-based method for solving the time-fractional diffusion equation. Zbl 07777024 Fardi, Mojtaba 1 2023 \(P_1\)-nonconforming quadrilateral finite element space with periodic boundary conditions. II: Application to the nonconforming heterogeneous multiscale method. Zbl 07777356 Yim, Jaeryun; Sheen, Dongwoo; Sim, Imbo 1 2023 Structure-preserving exponential wave integrator methods and the long-time convergence analysis for the Klein-Gordon-Dirac equation with the small coupling constant. Zbl 07777359 Li, Jiyong; Jin, Xiaoqian 1 2023 A Bochev-Dohrmann-Gunzburger stabilized method for Maxwell eigenproblem. Zbl 07777379 Du, Zhijie; Duan, Huoyuan; Wang, Can; Zhang, Qiuyu 1 2023 A simplified primal-dual weak Galerkin finite element method for Fokker-Planck-type equations. Zbl 1528.65113 Li, Dan; Wang, Chunmei 1 2023 High order accurate and convergent numerical scheme for the strongly anisotropic Cahn-Hilliard model. Zbl 07777387 Cheng, Kelong; Wang, Cheng; Wise, Steven M. 1 2023 A novel convenient finite difference method for shallow water waves derived by fifth-order Kortweg and de-Vries-type equation. Zbl 07779709 Poochinapan, Kanyuta; Wongsaijai, Ben 1 2023 Analysis of hybrid discontinuous Galerkin methods for linearized Navier-Stokes equations. Zbl 07779712 Shin, Dongwook; Jeon, Youngmok; Park, Eun-Jae 1 2023 A study of distributed-order time fractional diffusion models with continuous distribution weight functions. Zbl 07779715 Yu, Qiang; Turner, Ian; Liu, Fawang; Moroney, Timothy 1 2023 Finite difference schemes for the fourth-order parabolic equations with different boundary value conditions. Zbl 07779717 Lu, Xuan-ru; Gao, Guang-Hua; Sun, Zhi-Zhong 1 2023 Convergence analysis of a fast second-order time-stepping numerical method for two-dimensional nonlinear time-space fractional Schrödinger equation. Zbl 07779725 Zhang, Hui; Jiang, Xiaoyun 1 2023 Existence and uniqueness of solutions for fractional nonlinear hybrid impulsive system. Zbl 07777090 Gupta, Vidushi; Jarad, Fahd; Valliammal, Natarajan; Ravichandran, Chokkalingam; Nisar, Kottakkaran Sooppy 4 2022 European option pricing models described by fractional operators with classical and generalized Mittag-Leffler kernels. Zbl 07777095 Yavuz, Mehmet 4 2022 A stable computational approach to analyze semi-relativistic behavior of fractional evolutionary problems. Zbl 1527.65106 Hamid, Muhammad; Usman, Muhammad; Wang, Wei; Tian, Zhenfu 3 2022 Linearized stable spectral method to analyze two-dimensional nonlinear evolutionary and reaction-diffusion models. Zbl 1527.65105 Hamid, Muhammad; Usman, Muhammad; Haq, Rizwan UI; Tian, Zhenfu; Wang, Wei 3 2022 A new semi-analytic solution of fractional sixth order Drinfeld-Sokolov-Satsuma-Hirota equation. Zbl 07777091 Arafa, Anas; Hagag, Ahmed 3 2022 Jacobi collocation method for the fractional advection-dispersion equation arising in porous media. Zbl 07777106 Singh, Harendra 3 2022 Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems. Zbl 07778268 Dineshkumar, C.; Udhayakumar, R. 3 2022 A high-order weighted essentially nonoscillatory scheme based on exponential polynomials for nonlinear degenerate parabolic equations. Zbl 07778281 Abedian, Rooholah; Dehghan, Mehdi 3 2022 Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential. Zbl 07775895 Pei, Shuaichao; Hou, Yanren; Yan, Wenjing 2 2022 An interpolation method for the optimal control problem governed by the elliptic convection-diffusion equation. Zbl 07777078 Darehmiraki, Majid; Rezazadeh, Arezou; Ahmadian, Ali; Salahshour, Soheil 2 2022 A generalized differential quadrature algorithm for simulating magnetohydrodynamic peristaltic flow of blood-based nanofluid containing magnetite nanoparticles: a physiological application. Zbl 07777108 Ashraf, Muhammad Usman; Qasim, Muhammad; Wakif, Abderrahim; Afridi, Muhammad Idrees; Animasaun, Isaac L. 2 2022 Mathematical modeling for novel coronavirus (COVID-19) and control. Zbl 07778269 Alqarni, Marei Saeed; Alghamdi, Metib; Muhammad, Taseer; Alshomrani, Ali Saleh; Khan, Muhammad Altaf 2 2022 Heat and mass transfer analysis for bioconvective flow of Eyring Powell nanofluid over a Riga surface with nonlinear thermal features. Zbl 07778270 Usman; Khan, M. Ijaz; Shah, Faisal; Khan, Sami Ullah; Ghaffari, Abuzar; Chu, Yu-Ming 2 2022 Numerical solution of singularly perturbed 2D parabolic initial-boundary-value problems based on reproducing kernel theory: error and stability analysis. Zbl 07778275 Fardi, Mojtaba; Ghasemi, Mehdi 2 2022 On the nondifferentiable exact solutions to Schamel’s equation with local fractional derivative on Cantor sets. Zbl 07778295 Ghanbari, Behzad 2 2022 Numerical analysis of a second order ensemble method for evolutionary magnetohydrodynamics equations at small magnetic Reynolds number. Zbl 07778302 Carter, John; Jiang, Nan 2 2022 Decoupled and linearized scalar auxiliary variable finite element method for the time-dependent incompressible magnetohydrodynamic equations: unconditional stability and convergence analysis. Zbl 07778305 Zhang, Tong; Yang, Jinting 2 2022 Pattern selection in the Schnakenberg equations: from normal to anomalous diffusion. Zbl 07779681 Khudhair, Hatim K.; Zhang, Yanzhi; Fukawa, Nobuyuki 2 2022 A fractional model for anomalous diffusion with increased variability: analysis, algorithms and applications to interface problems. Zbl 07779691 D’Elia, Marta; Glusa, Christian 2 2022 Additive Schwarz preconditioners for \(C^0\) Interior penalty methods for the obstacle problem of clamped Kirchhoff plates. Zbl 07775896 Brenner, Susanne C.; Sung, Li-Yeng; Wang, Kening 1 2022 Fully spectral-Galerkin method for the one- and two-dimensional fourth-order time-fractional partial integro-differential equations with a weakly singular kernel. Zbl 07777079 Fakhar-Izadi, Farhad 1 2022 Numerical solution of fractional partial differential equations via Haar wavelet. Zbl 07777082 Zada, Laique; Aziz, Imran 1 2022 On the asymptotic behavior of a second-order general differential equation. Zbl 07777084 Say, Fatih 1 2022 Numerical and mathematical analysis of induction motor by means of AB-fractal-fractional differentiation actuated by drilling system. Zbl 07777087 Abro, Kashif Ali; Atangana, Abdon 1 2022 Numerical simulation of a nonlinear coupled differential system describing a convective flow of Casson gold-blood nanofluid through a stretched rotating rigid disk in the presence of Lorentz forces and nonlinear thermal radiation. Zbl 07777088 Khan, Umair; Bilal, Sardar; Zaib, A.; Makinde, O. D.; Wakif, Abderrahim 1 2022 Numerical simulation for entropy optimized nonlinear radiative flow of GO-\((\text{Al}_2\text{O}_3)\) magneto nanomaterials with auto catalysis chemical reaction. Zbl 07777089 Shaw, Sachin; Mabood, Fazle; Muhammad, Taseer; Nayak, Manoj Kumar; Alghamdi, Metib 1 2022 Numerical solution of fuzzy fractional diffusion equation by Chebyshev spectral method. Zbl 07777098 Kumar, Sachin 1 2022 New results concerning to approximate controllability of fractional integro-differential evolution equations of order \(1 < r < 2\). Zbl 07777099 Mohan Raja, M.; Vijayakumar, V. 1 2022 A numerical analysis for fractional model of the spread of pests in tea plants. Zbl 07777101 Kumar, Sunil; Kumar, Ajay; Jleli, Mohamed 1 2022 Half inverse problem for diffusion operators with jump conditions dependent on the spectral parameter. Zbl 07777103 Ergün, Abdullah; Amirov, Rauf 1 2022 Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water-based nanofluids with metal/metal oxide nanomaterials: a proper application of the revised two-phase nanofluid model with convective heating and through-flow boundary conditions. Zbl 07777105 Wakif, Abderrahim; Sehaqui, Rachid 1 2022 A formally second-order backward differentiation formula sinc-collocation method for the Volterra integro-differential equation with a weakly singular kernel based on the double exponential transformation. Zbl 07778273 Qiu, Wenlin; Xu, Da; Guo, Jing 1 2022 Numerical simulation of two-dimensional and three-dimensional generalized Klein-Gordon-Zakharov equations with power law nonlinearity via a meshless collocation method based on barycentric rational interpolation. Zbl 07778285 Oruç, Ömer 1 2022 Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators. Zbl 07778291 Abro, Kashif Ali 1 2022 Numerical analysis for a class of coupled system of singularly perturbed time-dependent convection-diffusion equations with a discontinuous source term. Zbl 07778303 Rao, S. Chandra Sekhara; Chawla, Sheetal; Chaturvedi, Abhay Kumar 1 2022 Numerical solution of fractional Dullin-Gottwald-Holm equation for solitary shallow water waves. Zbl 07778308 Saha Ray, Santanu; Sagar, B. 1 2022 Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects. Zbl 07779673 Jiang, Kun; Ju, Lili; Li, Jingwei; Li, Xiao 1 2022 Second-order, fully decoupled, linearized, and unconditionally stable scalar auxiliary variable schemes for Cahn-Hilliard-Darcy system. Zbl 07779674 Gao, Yali; He, Xiaoming; Nie, Yufeng 1 2022 Analysis of the variable step method of Dahlquist, Liniger and Nevanlinna for fluid flow. Zbl 07779676 Layton, William; Pei, Wenlong; Qin, Yi; Trenchea, Catalin 1 2022 A new study on existence and uniqueness of nonlocal fractional delay differential systems of order \(1 < r < 2\) in Banach spaces. Zbl 07775996 Kavitha Williams, W.; Vijayakumar, V.; Udhayakumar, R.; Nisar, Kottakkaran Sooppy 14 2021 Results on approximate controllability results for second-order Sobolev-type impulsive neutral differential evolution inclusions with infinite delay. Zbl 07776009 Vijayakumar, V.; Panda, Sumati Kumari; Nisar, Kottakkaran Sooppy; Baskonus, Haci Mehmet 12 2021 The reducing rank method to solve third-order Duffing equation with the homotopy perturbation. Zbl 07776044 He, Ji-Huan; El-Dib, Yusry O. 11 2021 A new exploration on existence of Sobolev-type Hilfer fractional neutral integro-differential equations with infinite delay. Zbl 07777720 Vijayakumar, V.; Udhayakumar, R. 11 2021 A wavelet based numerical scheme for fractional order SEIR epidemic of measles by using Genocchi polynomials. Zbl 07776012 Kumar, Sunil; Kumar, Ranbir; Osman, M. S.; Samet, Bessem 10 2021 New numerical simulation for fractional Benney-Lin equation arising in falling film problems using two novel techniques. Zbl 07777696 Gao, Wei; Veeresha, Pundikala; Prakasha, Doddabhadrappla Gowda; Baskonus, Haci Mehmet 8 2021 ...and 1424 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 14,486 Authors 283 Dehghan Takht Fooladi, Mehdi 110 Shi, Dongyang 105 He, Yinnian 89 Huang, Yunqing 86 Wang, Hong 83 Gatica, Gabriel N. 79 Zhang, Zhimin 78 Mohanty, Ranjan Kumar 75 Băleanu, Dumitru I. 71 Feng, Xinlong 69 Abbaszadeh, Mostafa 69 Chen, Yanping 67 Rui, Hongxing 66 Li, Hong 63 Li, Jian 60 Sun, Zhizhong 58 Chen, Zhangxin 58 Li, Jichun 58 Liu, Yang 56 Ruiz-Baier, Ricardo 55 Huang, Pengzhan 55 Rebholz, Leo G. 55 Xu, Da 52 Liu, Fawang 52 Ye, Xiu 50 Hou, Yanren 49 Yang, Xiaofeng 45 Yuan, Guangwei 45 Zhang, Shangyou 44 Zhang, Tong 43 Li, Zi-Cai 41 Heuer, Norbert 41 Khaliq, Abdul Q. 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