Gupta, Aastha; Kaushik, Aditya A higher-order hybrid finite difference method based on grid equidistribution for fourth-order singularly perturbed differential equations. (English) Zbl 1486.65080 J. Appl. Math. Comput. 68, No. 2, 1163-1191 (2022). MSC: 65L11 65L10 65L12 PDF BibTeX XML Cite \textit{A. Gupta} and \textit{A. Kaushik}, J. Appl. Math. Comput. 68, No. 2, 1163--1191 (2022; Zbl 1486.65080) Full Text: DOI OpenURL
Zhang, Yong; Bao, Xiaobing; Liu, Li-Bin; Liang, Zhifang Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid. (English) Zbl 1484.65154 AIMS Math. 6, No. 8, 8611-8624 (2021). MSC: 65L12 34A08 65L05 65L20 PDF BibTeX XML Cite \textit{Y. Zhang} et al., AIMS Math. 6, No. 8, 8611--8624 (2021; Zbl 1484.65154) Full Text: DOI OpenURL
Long, Guangqing; Liu, Li-Bin; Huang, Zaitang Richardson extrapolation method on an adaptive grid for singularly perturbed Volterra integro-differential equations. (English) Zbl 07379882 Numer. Funct. Anal. Optim. 42, No. 7, 739-757 (2021). MSC: 65L10 65L12 65N30 PDF BibTeX XML Cite \textit{G. Long} et al., Numer. Funct. Anal. Optim. 42, No. 7, 739--757 (2021; Zbl 07379882) Full Text: DOI OpenURL
Khayutin, Ilya Equidistribution on Kuga-Sato varieties of torsion points on CM elliptic curves. (English) Zbl 07367682 J. Eur. Math. Soc. (JEMS) 23, No. 9, 2949-3016 (2021). MSC: 11G18 11G05 37A17 PDF BibTeX XML Cite \textit{I. Khayutin}, J. Eur. Math. Soc. (JEMS) 23, No. 9, 2949--3016 (2021; Zbl 07367682) Full Text: DOI arXiv OpenURL
Gupta, Aastha; Kaushik, Aditya A robust spline difference method for Robin-type reaction-diffusion problem using grid equidistribution. (English) Zbl 07330169 Appl. Math. Comput. 390, Article ID 125597, 17 p. (2021). MSC: 65-XX 41-XX PDF BibTeX XML Cite \textit{A. Gupta} and \textit{A. Kaushik}, Appl. Math. Comput. 390, Article ID 125597, 17 p. (2021; Zbl 07330169) Full Text: DOI OpenURL
Avijit, D.; Natesan, S. SDFEM for singularly perturbed parabolic initial-boundary-value problems on equidistributed grids. (English) Zbl 1451.65141 Calcolo 57, No. 3, Paper No. 23, 25 p. (2020). MSC: 65M60 65M12 65M50 PDF BibTeX XML Cite \textit{D. Avijit} and \textit{S. Natesan}, Calcolo 57, No. 3, Paper No. 23, 25 p. (2020; Zbl 1451.65141) Full Text: DOI OpenURL
Liu, Li-Bin; Liang, Zhifang; Long, Guangqing; Liang, Ying Convergence analysis of a finite difference scheme for a Riemann-Liouville fractional derivative two-point boundary value problem on an adaptive grid. (English) Zbl 1434.65096 J. Comput. Appl. Math. 375, Article ID 112809, 8 p. (2020). MSC: 65L10 65L12 65L20 26A33 PDF BibTeX XML Cite \textit{L.-B. Liu} et al., J. Comput. Appl. Math. 375, Article ID 112809, 8 p. (2020; Zbl 1434.65096) Full Text: DOI OpenURL
Gowrisankar, S.; Natesan, Srinivasan An efficient robust numerical method for singularly perturbed Burgers’ equation. (English) Zbl 1429.65182 Appl. Math. Comput. 346, 385-394 (2019). MSC: 65M06 35B25 35Q53 65M12 PDF BibTeX XML Cite \textit{S. Gowrisankar} and \textit{S. Natesan}, Appl. Math. Comput. 346, 385--394 (2019; Zbl 1429.65182) Full Text: DOI OpenURL
Mao, Zhi; Liu, Libin An adaptive moving grid algorithm for a system of singularly perturbed problems. (Chinese. English summary) Zbl 1438.65228 Nat. Sci. J. Xiangtan Univ. 41, No. 1, 64-71 (2019). MSC: 65M50 65M12 35K57 PDF BibTeX XML Cite \textit{Z. Mao} and \textit{L. Liu}, Nat. Sci. J. Xiangtan Univ. 41, No. 1, 64--71 (2019; Zbl 1438.65228) Full Text: DOI OpenURL
Mohapatra, J.; Mahalik, M. K. An initial value method for solving singularly perturbed boundary value problems using adaptive grids. (English) Zbl 1444.65040 Comput. Math. Model. 29, No. 1, 48-58 (2018). MSC: 65L10 65L50 34E20 PDF BibTeX XML Cite \textit{J. Mohapatra} and \textit{M. K. Mahalik}, Comput. Math. Model. 29, No. 1, 48--58 (2018; Zbl 1444.65040) Full Text: DOI OpenURL
Das, Pratibhamoy; Natesan, Srinivasan Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations. (English) Zbl 1317.65160 Int. J. Comput. Math. 92, No. 3, 562-578 (2015). MSC: 65L10 PDF BibTeX XML Cite \textit{P. Das} and \textit{S. Natesan}, Int. J. Comput. Math. 92, No. 3, 562--578 (2015; Zbl 1317.65160) Full Text: DOI OpenURL
Gowrisankar, S.; Natesan, Srinivasan Robust numerical scheme for singularly perturbed convection-diffusion parabolic initial-boundary-value problems on equidistributed grids. (English) Zbl 1352.65292 Comput. Phys. Commun. 185, No. 7, 2008-2019 (2014). MSC: 65M12 65M06 35K20 PDF BibTeX XML Cite \textit{S. Gowrisankar} and \textit{S. Natesan}, Comput. Phys. Commun. 185, No. 7, 2008--2019 (2014; Zbl 1352.65292) Full Text: DOI OpenURL
Gowrisankar, S.; Natesan, Srinivasan A robust numerical scheme for singularly perturbed delay parabolic initial-boundary-value problems on equidistributed grids. (English) Zbl 1312.65135 ETNA, Electron. Trans. Numer. Anal. 41, 376-395 (2014). MSC: 65M06 35K20 35R10 35B25 65M12 65M15 PDF BibTeX XML Cite \textit{S. Gowrisankar} and \textit{S. Natesan}, ETNA, Electron. Trans. Numer. Anal. 41, 376--395 (2014; Zbl 1312.65135) Full Text: EMIS OpenURL
Gowrisankar, S.; Natesan, Srinivasan Uniformly convergent numerical method for singularly perturbed parabolic initial-boundary-value problems with equidistributed grids. (English) Zbl 1299.65211 Int. J. Comput. Math. 91, No. 3, 553-577 (2014). MSC: 65M12 65M06 65M50 35K57 76D10 76M20 PDF BibTeX XML Cite \textit{S. Gowrisankar} and \textit{S. Natesan}, Int. J. Comput. Math. 91, No. 3, 553--577 (2014; Zbl 1299.65211) Full Text: DOI OpenURL
Khakimzyanov, Gayaz Salimovich; Shokina, Nina Yur’evna Adaptive grid method for one-dimensional shallow water equations. (Russian. English summary) Zbl 1421.76173 Vychisl. Tekhnol. 18, No. 3, 54-79 (2013). MSC: 76M25 76B15 PDF BibTeX XML Cite \textit{G. S. Khakimzyanov} and \textit{N. Y. Shokina}, Vychisl. Tekhnol. 18, No. 3, 54--79 (2013; Zbl 1421.76173) Full Text: Link OpenURL
Gowrisankar, S.; Natesan, Srinivasan The parameter uniform numerical method for singularly perturbed parabolic reaction-diffusion problems on equidistributed grids. (English) Zbl 1311.65111 Appl. Math. Lett. 26, No. 11, 1053-1060 (2013). MSC: 65M06 35B25 35K57 65M12 65M50 65M15 PDF BibTeX XML Cite \textit{S. Gowrisankar} and \textit{S. Natesan}, Appl. Math. Lett. 26, No. 11, 1053--1060 (2013; Zbl 1311.65111) Full Text: DOI OpenURL
Sommer, Anna Fedorovna; Shokina, Nina Yur’evna On some problems of construction of two-dimensional difference schemes on moving grids. (Russian. English summary) Zbl 1420.65102 Vychisl. Tekhnol. 17, No. 4, 88-108 (2012). MSC: 65M60 PDF BibTeX XML Cite \textit{A. F. Sommer} and \textit{N. Y. Shokina}, Vychisl. Tekhnol. 17, No. 4, 88--108 (2012; Zbl 1420.65102) Full Text: Link OpenURL
Khakimzyanov, Gayaz Salĭmovich; Shokina, Nina Yur’evna Some notes on monotonicity preserving schemes. (Russian. English summary) Zbl 1420.65084 Vychisl. Tekhnol. 17, No. 2, 78-98 (2012). MSC: 65L99 PDF BibTeX XML Cite \textit{G. S. Khakimzyanov} and \textit{N. Y. Shokina}, Vychisl. Tekhnol. 17, No. 2, 78--98 (2012; Zbl 1420.65084) Full Text: Link OpenURL
Das, Pratibhamoy; Natesan, Srinivasan Higher-order parameter uniform convergent schemes for Robin type reaction-diffusion problems using adaptively generated grid. (English) Zbl 1359.65123 Int. J. Comput. Methods 9, No. 4, Article ID 1250052, 27 p. (2012). MSC: 65L11 65L50 65L10 PDF BibTeX XML Cite \textit{P. Das} and \textit{S. Natesan}, Int. J. Comput. Methods 9, No. 4, Article ID 1250052, 27 p. (2012; Zbl 1359.65123) Full Text: DOI OpenURL
Yuan, Xuefei; Jardin, Stephen C.; Keyes, David E. Numerical simulation of four-field extended magnetohydrodynamics in dynamically adaptive curvilinear coordinates via Newton-Krylov-Schwarz. (English) Zbl 1277.49037 J. Comput. Phys. 231, No. 17, 5822-5853 (2012). MSC: 49M15 35G20 65M99 PDF BibTeX XML Cite \textit{X. Yuan} et al., J. Comput. Phys. 231, No. 17, 5822--5853 (2012; Zbl 1277.49037) Full Text: DOI OpenURL
Delzanno, Gian Luca; Finn, John M. The fluid dynamic approach to equidistribution methods for grid adaptation. (English) Zbl 1217.65184 Comput. Phys. Commun. 182, No. 2, 330-346 (2011). MSC: 65M50 35K96 65M55 65F08 PDF BibTeX XML Cite \textit{G. L. Delzanno} and \textit{J. M. Finn}, Comput. Phys. Commun. 182, No. 2, 330--346 (2011; Zbl 1217.65184) Full Text: DOI OpenURL
Chadha, Naresh M.; Kopteva, Natalia A robust grid equidistribution method for a one-dimensional singularly perturbed semilinear reaction-diffusion problem. (English) Zbl 1211.65099 IMA J. Numer. Anal. 31, No. 1, 188-211 (2011). Reviewer: Abdallah Bradji (Annaba) MSC: 65L10 65L70 65L50 65L12 34B15 65L11 34E15 PDF BibTeX XML Cite \textit{N. M. Chadha} and \textit{N. Kopteva}, IMA J. Numer. Anal. 31, No. 1, 188--211 (2011; Zbl 1211.65099) Full Text: DOI Link OpenURL
Pulverer, Gernot; Söderlind, Gustaf; Weinmüller, Ewa Automatic grid control in adaptive BVP solvers. (English) Zbl 1206.65198 Numer. Algorithms 56, No. 1, 61-92 (2011). MSC: 65L50 65L10 34B15 34E15 65L70 PDF BibTeX XML Cite \textit{G. Pulverer} et al., Numer. Algorithms 56, No. 1, 61--92 (2011; Zbl 1206.65198) Full Text: DOI Link OpenURL
Delzanno, G. L.; Finn, J. M. Generalized Monge-Kantorovich optimization for grid generation and adaptation in \(L_p\). (English) Zbl 1220.49020 SIAM J. Sci. Comput. 32, No. 6, 3524-3547 (2010). MSC: 49M37 65K10 65N50 65Z05 PDF BibTeX XML Cite \textit{G. L. Delzanno} and \textit{J. M. Finn}, SIAM J. Sci. Comput. 32, No. 6, 3524--3547 (2010; Zbl 1220.49020) Full Text: DOI OpenURL
Liu, Ying; Chen, Yanping Convergence analysis for a singularly perturbed problem using the forward upwind difference scheme on adaptive meshes. (Chinese. English summary) Zbl 1212.65288 Nat. Sci. J. Xiangtan Univ. 31, No. 2, 8-11 (2009). MSC: 65L10 34B05 34E15 65L12 65L20 65L70 PDF BibTeX XML Cite \textit{Y. Liu} and \textit{Y. Chen}, Nat. Sci. J. Xiangtan Univ. 31, No. 2, 8--11 (2009; Zbl 1212.65288) OpenURL
Delzanno, G. L.; Chacón, L.; Finn, J. M.; Chung, Y.; Lapenta, G. An optimal robust equidistribution method for two-dimensional grid adaptation based on Monge-Kantorovich optimization. (English) Zbl 1155.65394 J. Comput. Phys. 227, No. 23, 9841-9864 (2008). MSC: 65N50 PDF BibTeX XML Cite \textit{G. L. Delzanno} et al., J. Comput. Phys. 227, No. 23, 9841--9864 (2008; Zbl 1155.65394) Full Text: DOI OpenURL
Chen, Long; Xu, Jinchao Stability and accuracy of adapted finite element methods for singularly perturbed problems. (English) Zbl 1146.65059 Numer. Math. 109, No. 2, 167-191 (2008). Reviewer: Srinivasan Natesan (Assam) MSC: 65L20 65L60 65L10 34B05 34E15 PDF BibTeX XML Cite \textit{L. Chen} and \textit{J. Xu}, Numer. Math. 109, No. 2, 167--191 (2008; Zbl 1146.65059) Full Text: DOI OpenURL
Kaushik, Aditya Pointwise uniformly convergent numerical treatment for the non-stationary Burger-Huxley equation using grid equidistribution. (English) Zbl 1128.65075 Int. J. Comput. Math. 84, No. 10, 1527-1546 (2007). Reviewer: Qin Mengzhao (Beijing) MSC: 65M20 65M06 65M12 65M15 35B25 35K55 65L06 PDF BibTeX XML Cite \textit{A. Kaushik}, Int. J. Comput. Math. 84, No. 10, 1527--1546 (2007; Zbl 1128.65075) Full Text: DOI OpenURL
Kopteva, Natalia Maximum norm a posteriori error estimates for a 1D singularly perturbed semilinear reaction-diffusion problem. (English) Zbl 1149.65066 IMA J. Numer. Anal. 27, No. 3, 576-592 (2007). Reviewer: I. N. Katz (St. Louis) MSC: 65L70 34B15 34E15 65L10 65L12 65L50 PDF BibTeX XML Cite \textit{N. Kopteva}, IMA J. Numer. Anal. 27, No. 3, 576--592 (2007; Zbl 1149.65066) Full Text: DOI OpenURL
Yamaleev, Nail K. Minimization of the truncation error by grid adaptation. (English) Zbl 0984.65126 J. Comput. Phys. 170, No. 2, 459-497 (2001). MSC: 65N50 65N06 PDF BibTeX XML Cite \textit{N. K. Yamaleev}, J. Comput. Phys. 170, No. 2, 459--497 (2001; Zbl 0984.65126) Full Text: DOI Link OpenURL
Linß, T. Uniform pointwise convergence of finite difference schemes using grid equidistribution. (English) Zbl 0984.65077 Computing 66, No. 1, 27-39 (2001). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65L10 65L12 65L20 65L50 34B15 34E15 PDF BibTeX XML Cite \textit{T. Linß}, Computing 66, No. 1, 27--39 (2001; Zbl 0984.65077) Full Text: DOI OpenURL
Kopteva, Natalia Maximum norm a posteriori error estimates for a one-dimensional convection-diffusion problem. (English) Zbl 1003.65091 SIAM J. Numer. Anal. 39, No. 2, 423-441 (2001). Reviewer: Kevin Burrage (Brisbane) MSC: 65L70 34B15 34E15 65L50 65L10 65L12 PDF BibTeX XML Cite \textit{N. Kopteva}, SIAM J. Numer. Anal. 39, No. 2, 423--441 (2001; Zbl 1003.65091) Full Text: DOI OpenURL
Soni, Bharat K.; Koomullil, Roy; Thompson, David S.; Thornburg, Hugh Solution adaptive grid strategies based on point redistribution. (English) Zbl 1007.76070 Comput. Methods Appl. Mech. Eng. 189, No. 4, 1183-1204 (2000). MSC: 76M99 65M50 65N50 65Y05 PDF BibTeX XML Cite \textit{B. K. Soni} et al., Comput. Methods Appl. Mech. Eng. 189, No. 4, 1183--1204 (2000; Zbl 1007.76070) Full Text: DOI OpenURL
Khakimzyanov, G. S.; Shokina, N. Yu. Equidistribution method for the construction of adaptive grids. (English) Zbl 0943.65140 Russ. J. Numer. Anal. Math. Model. 14, No. 4, 339-358 (1999). Reviewer: A.L.Pletea (Iaşi) MSC: 65N50 65L50 65L12 PDF BibTeX XML Cite \textit{G. S. Khakimzyanov} and \textit{N. Yu. Shokina}, Russ. J. Numer. Anal. Math. Model. 14, No. 4, 339--358 (1999; Zbl 0943.65140) Full Text: DOI OpenURL
Kania, Lee Elliptic adaptive grid generation and area equidistribution. (English) Zbl 0946.76080 Int. J. Numer. Methods Fluids 30, No. 5, 481-491 (1999). MSC: 76M99 76N15 65M50 65N50 PDF BibTeX XML Cite \textit{L. Kania}, Int. J. Numer. Methods Fluids 30, No. 5, 481--491 (1999; Zbl 0946.76080) Full Text: DOI OpenURL
Khakimzyanov, G. S.; Shokina, N. Yu. Equidistribution method for constructing adapting grids. (Russian. English summary) Zbl 0917.65092 Vychisl. Tekhnol. 3, No. 6, 63-81 (1998). MSC: 65N50 35J65 65N06 PDF BibTeX XML Cite \textit{G. S. Khakimzyanov} and \textit{N. Yu. Shokina}, Vychisl. Tekhnol. 3, No. 6, 63--81 (1998; Zbl 0917.65092) OpenURL
Castillo, José; Pedersen, Erik M. Solution adaptive direct variational grids for fluid flow calculations. (English) Zbl 0856.76039 J. Comput. Appl. Math. 67, No. 2, 343-370 (1996). MSC: 76M20 76H05 65F10 PDF BibTeX XML Cite \textit{J. Castillo} and \textit{E. M. Pedersen}, J. Comput. Appl. Math. 67, No. 2, 343--370 (1996; Zbl 0856.76039) Full Text: DOI OpenURL
Mackenzie, J. A.; Süli, Endre Reliable error control for adaptive computations of the compressible Euler equations. (English) Zbl 0881.76073 Morton, K. W. (ed.) et al., Numerical methods for fluid dynamics V. Proceedings of the conference, Oxford, UK, April 1995. Oxford: Clarendon Press. 473-479 (1995). Reviewer: W.Schönauer (Karlsruhe) MSC: 76M25 76N10 65M15 PDF BibTeX XML Cite \textit{J. A. Mackenzie} and \textit{E. Süli}, in: Numerical methods for fluid dynamics V. Proceedings of the conference, Oxford, UK, April 1995. Oxford: Clarendon Press. 473--479 (1995; Zbl 0881.76073) OpenURL
Yang, Jiann-Cherng; Soni, Bharat K. Structured adaptive grid generation. (English) Zbl 0811.65077 Appl. Math. Comput. 65, No. 1-3, 265-278 (1994). MSC: 65M50 65M06 35L67 76L05 PDF BibTeX XML Cite \textit{J.-C. Yang} and \textit{B. K. Soni}, Appl. Math. Comput. 65, No. 1--3, 265--278 (1994; Zbl 0811.65077) Full Text: DOI OpenURL
Baines, M. J. Moving finite elements. (English) Zbl 0817.65082 Monographs on Numerical Analysis. Oxford Science Publications. Oxford: Clarendon Press. xi, 226 p. (1994). Reviewer: S.F.Sburlan (Granada) MSC: 65M60 65-02 65M15 35G10 35K25 35L15 35K15 35L67 PDF BibTeX XML Cite \textit{M. J. Baines}, Moving finite elements. Oxford: Clarendon Press (1994; Zbl 0817.65082) OpenURL
Huang, Weizhang; Sloan, David M. A simple adaptive grid method in two dimensions. (English) Zbl 0809.65096 SIAM J. Sci. Comput. 15, No. 4, 776-797 (1994). Reviewer: K.T.S.Iyengar (Bangalore) MSC: 65M50 PDF BibTeX XML Cite \textit{W. Huang} and \textit{D. M. Sloan}, SIAM J. Sci. Comput. 15, No. 4, 776--797 (1994; Zbl 0809.65096) Full Text: DOI Link OpenURL
Moukalled, F.; Acharya, S. A local adaptive grid procedure for incompressible flows with multigridding and equidistribution concepts. (English) Zbl 0737.76051 Int. J. Numer. Methods Fluids 13, No. 9, 1085-1111 (1991). MSC: 76M20 76B15 65N50 PDF BibTeX XML Cite \textit{F. Moukalled} and \textit{S. Acharya}, Int. J. Numer. Methods Fluids 13, No. 9, 1085--1111 (1991; Zbl 0737.76051) Full Text: DOI OpenURL
Ramos, J. I. Finite element methods for one-dimensional combustion problems. (English) Zbl 0705.76057 Int. J. Numer. Methods Fluids 11, No. 6, 893-906 (1990). MSC: 76L05 76M10 80A25 PDF BibTeX XML Cite \textit{J. I. Ramos}, Int. J. Numer. Methods Fluids 11, No. 6, 893--906 (1990; Zbl 0705.76057) Full Text: DOI OpenURL
Eiseman, Peter R. Adaptive grid generation. (English) Zbl 0636.65126 Comput. Methods Appl. Mech. Eng. 64, 321-376 (1987). Reviewer: J.Král MSC: 65N50 65-02 PDF BibTeX XML Cite \textit{P. R. Eiseman}, Comput. Methods Appl. Mech. Eng. 64, 321--376 (1987; Zbl 0636.65126) Full Text: DOI OpenURL
Shyy, Wei An adaptive grid method for Navier-Stokes flow computation. (English) Zbl 0607.76030 Appl. Math. Comput. 21, 201-219 (1987). MSC: 76D10 76M99 PDF BibTeX XML Cite \textit{W. Shyy}, Appl. Math. Comput. 21, 201--219 (1987; Zbl 0607.76030) Full Text: DOI OpenURL
Shyy, Wei An adaptive grid method for Navier-Stokes flow computation. II. Grid addition. (English) Zbl 0619.76032 Appl. Numer. Math. 2, 9-19 (1986). MSC: 76D05 76M99 65Gxx PDF BibTeX XML Cite \textit{W. Shyy}, Appl. Numer. Math. 2, 9--19 (1986; Zbl 0619.76032) Full Text: DOI OpenURL