High order parameter-robust numerical method for time dependent singularly perturbed reaction–diffusion problems

Mukesh Kumar; S. Chandra Sekhara Rao

doi:10.1007/s00607-010-0104-1

High order parameter-robust numerical method for time dependent singularly perturbed reaction–diffusion problems

Computing ◽

10.1007/s00607-010-0104-1 ◽

2010 ◽

Vol 90 (1-2) ◽

pp. 15-38 ◽

Cited By ~ 7

Author(s):

Mukesh Kumar ◽

S. Chandra Sekhara Rao

Keyword(s):

Numerical Method ◽

Order Parameter ◽

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Time Dependent ◽

Diffusion Problems

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High order parameter-robust numerical method for singularly perturbed reaction–diffusion problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.01.121 ◽

2010 ◽

Vol 216 (4) ◽

pp. 1036-1046 ◽

Cited By ~ 2

Author(s):

Mukesh Kumar ◽

S. Chandra Sekhara Rao

Keyword(s):

Numerical Method ◽

Order Parameter ◽

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Diffusion Problems

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A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction–diffusion problems

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.10.072 ◽

2012 ◽

Vol 218 (9) ◽

pp. 5067-5080 ◽

Cited By ~ 8

Author(s):

C. Clavero ◽

J.L. Gracia

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Diffusion Problems

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High-Order Compact Finite-Difference Scheme for Singularly-Perturbed Reaction-Diffusion Problems on a New Mesh of Shishkin Type

Journal of Optimization Theory and Applications ◽

10.1007/s10957-009-9547-y ◽

2009 ◽

Vol 143 (1) ◽

pp. 123-147 ◽

Cited By ~ 13

Author(s):

V. Kumar

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Compact Finite Difference Scheme ◽

Compact Finite Difference ◽

Diffusion Problems

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A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems

Computational and Applied Mathematics ◽

10.1007/s40314-013-0033-7 ◽

2013 ◽

Vol 32 (3) ◽

pp. 509-519 ◽

Cited By ~ 5

Author(s):

Justin B. Munyakazi ◽

Kailash C. Patidar

Keyword(s):

Numerical Method ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Diffusion Problems

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A robust overlapping Schwarz domain decomposition algorithm for time-dependent singularly perturbed reaction–diffusion problems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2013.10.053 ◽

2014 ◽

Vol 261 ◽

pp. 127-138 ◽

Cited By ~ 14

Author(s):

Sunil Kumar ◽

S. Chandra Sekhara Rao

Keyword(s):

Domain Decomposition ◽

Reaction Diffusion ◽

Decomposition Algorithm ◽

Singularly Perturbed ◽

Time Dependent ◽

Domain Decomposition Algorithm ◽

Diffusion Problems ◽

Overlapping Schwarz

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Robust High Order Convergence of an Overlapping Schwarz Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems

Journal of Computational Mathematics ◽

10.4208/jcm.1307-m3787 ◽

2013 ◽

Vol 31 (5) ◽

pp. 509-521 ◽

Cited By ~ 5

Author(s):

S. Chandra Sekhara Rao and Sunil Kumar

Keyword(s):

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Order Convergence ◽

Schwarz Method ◽

High Order Convergence ◽

Diffusion Problems ◽

Overlapping Schwarz

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Second Order Uniformly Convergent Numerical Method for a Coupled System of Singularly Perturbed Reaction-Diffusion Problems with Discontinuous Source Term

Lecture Notes in Computational Science and Engineering - Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2014 ◽

10.1007/978-3-319-25727-3_18 ◽

2015 ◽

pp. 233-244 ◽

Cited By ~ 1

Author(s):

S. Chandra Sekhara Rao ◽

Sheetal Chawla

Keyword(s):

Numerical Method ◽

Source Term ◽

Reaction Diffusion ◽

Coupled System ◽

Second Order ◽

Singularly Perturbed ◽

Discontinuous Source Term ◽

Uniformly Convergent ◽

Diffusion Problems

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High‐order discrete‐time orthogonal spline collocation methods for singularly perturbed 1D parabolic reaction–diffusion problems

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22438 ◽

2019 ◽

Vol 36 (3) ◽

pp. 495-523

Author(s):

Pankaj Mishra ◽

Kapil K. Sharma ◽

Amiya K. Pani ◽

Graeme Fairweather

Keyword(s):

Discrete Time ◽

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Collocation Methods ◽

Spline Collocation ◽

Orthogonal Spline Collocation ◽

Diffusion Problems

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A high order uniformly convergent alternating direction scheme for time dependent reaction–diffusion singularly perturbed problems

Numerische Mathematik ◽

10.1007/s00211-007-0083-0 ◽

2007 ◽

Vol 107 (1) ◽

pp. 1-25 ◽

Cited By ~ 18

Author(s):

B. Bujanda ◽

C. Clavero ◽

J. L. Gracia ◽

J. C. Jorge

Keyword(s):

Reaction Diffusion ◽

High Order ◽

Singularly Perturbed ◽

Time Dependent ◽

Singularly Perturbed Problems ◽

Alternating Direction ◽

Uniformly Convergent

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A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems

IMA Journal of Numerical Analysis ◽

10.1093/imanum/23.4.627 ◽

2003 ◽

Vol 23 (4) ◽

pp. 627-644 ◽

Cited By ~ 71

Author(s):

N. Madden

Keyword(s):

Numerical Method ◽

Reaction Diffusion ◽

Coupled System ◽

Singularly Perturbed ◽

Linear Reaction ◽

Uniformly Convergent ◽

Diffusion Problems

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