A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction–convection–diffusion systems with two small parameters and discontinuous source terms

Journal of Mathematical Chemistry ◽

10.1007/s10910-019-01094-1 ◽

2019 ◽

Vol 58 (3) ◽

pp. 663-685 ◽

Author(s):

K. Aarthika ◽

V. Shanthi ◽

Higinio Ramos

Keyword(s):

Difference Scheme ◽

Singularly Perturbed ◽

Source Terms ◽

Convection Diffusion ◽

Diffusion Systems ◽

Small Parameters

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A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations

Numerical Methods for Partial Differential Equations ◽

10.1002/num.22732 ◽

2020 ◽

Author(s):

Kamalesh Kumar ◽

Pramod Chakravarthy Podila

Keyword(s):

Finite Difference ◽

Error Analysis ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singularly Perturbed ◽

Diffusion Equations ◽

Two Dimensional ◽

Convection Diffusion

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Difference scheme for a singularly perturbed parabolic convection–diffusion equation in the presence of perturbations

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542515110159 ◽

2015 ◽

Vol 55 (11) ◽

pp. 1842-1856 ◽

Author(s):

G. I. Shishkin

Keyword(s):

Diffusion Equation ◽

Difference Scheme ◽

Singularly Perturbed ◽

Convection Diffusion ◽

Convection Diffusion Equation

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Finite difference scheme for third order singularly perturbed delay differential equation of convection diffusion type with integral boundary condition

Journal of Applied Mathematics and Computing ◽

10.1007/s12190-019-01239-0 ◽

2019 ◽

Vol 61 (1-2) ◽

pp. 73-86 ◽

Author(s):

Elango Sekar ◽

Ayyadurai Tamilselvan

Keyword(s):

Differential Equation ◽

Boundary Condition ◽

Finite Difference ◽

Difference Scheme ◽

Singularly Perturbed ◽

Third Order ◽

Diffusion Type ◽

Integral Boundary ◽

Convection Diffusion ◽

Delay Differential

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A uniformly convergent finite difference scheme for Robin type singularly perturbed parabolic convection diffusion problem

Mathematics and Computers in Simulation ◽

10.1016/j.matcom.2020.03.003 ◽

2020 ◽

Vol 174 ◽

pp. 218-232

Author(s):

Nana Adjoah Mbroh ◽

Suares Clovis Oukouomi Noutchie ◽

Rodrigue Yves M’pika Massoukou

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Diffusion Problem ◽

Singularly Perturbed ◽

Convection Diffusion ◽

Uniformly Convergent

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Analysis of an upwind finite-difference scheme for a system of coupled singularly perturbed convection-diffusion equations

Computing ◽

10.1007/s00607-006-0215-x ◽

2006 ◽

Vol 79 (1) ◽

pp. 23-32 ◽

Author(s):

T. Linß

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singularly Perturbed ◽

Diffusion Equations ◽

Convection Diffusion ◽

Upwind Finite Difference

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A finite-difference scheme for a coupled system of singularly perturbed time-dependent reaction–diffusion equations with discontinuous source terms

International Journal of Computer Mathematics ◽

10.1080/00207160.2020.1733538 ◽

2020 ◽

pp. 1-16

Author(s):

K. Aarthika ◽

V. Shanthi ◽

Higinio Ramos

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Reaction Diffusion ◽

Coupled System ◽

Reaction Diffusion Equations ◽

Singularly Perturbed ◽

Time Dependent ◽

Diffusion Equations ◽

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An almost third order finite difference scheme for singularly perturbed reaction–diffusion systems

Journal of Computational and Applied Mathematics ◽

10.1016/j.cam.2010.03.011 ◽

2010 ◽

Vol 234 (8) ◽

pp. 2501-2515 ◽

Author(s):

C. Clavero ◽

J.L. Gracia ◽

F.J. Lisbona

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Reaction Diffusion ◽

Singularly Perturbed ◽

Third Order ◽

Reaction Diffusion Systems ◽

Diffusion Systems

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A parameter-uniform hybrid finite difference scheme for singularly perturbed system of parabolic convection-diffusion problems

International Journal of Computer Mathematics ◽

10.1080/00207160.2019.1597972 ◽

2019 ◽

Vol 97 (4) ◽

pp. 875-905 ◽

Author(s):

Maneesh Kumar Singh ◽

Srinivasan Natesan

Keyword(s):

Finite Difference ◽

Difference Scheme ◽

Finite Difference Scheme ◽

Singularly Perturbed ◽

Singularly Perturbed System ◽

Convection Diffusion ◽

Perturbed System ◽

Diffusion Problems

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Hybrid Difference Scheme for Singularly Perturbed Convection Diffusion Boundary Turning Point Problems with Discontinuous Source Term

International Journal of Applied and Computational Mathematics ◽

10.1007/s40819-019-0676-1 ◽

2019 ◽

Vol 5 (3) ◽

Author(s):

G. Janani Jayalakshmi ◽

A. Tamilselvan

Keyword(s):

Difference Scheme ◽

Turning Point ◽

Source Term ◽

Singularly Perturbed ◽

Diffusion Boundary ◽

Convection Diffusion ◽

Discontinuous Source Term

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The Sdfem for a Convection-diffusion Problem with Two Small Parameters

Computational Methods in Applied Mathematics ◽

10.2478/cmam-2003-0029 ◽

2003 ◽

Vol 3 (3) ◽

pp. 443-458 ◽

Author(s):

Hans-Görg Roos ◽

Zorica Uzelac

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Numerical Experiments ◽

Diffusion Problem ◽

Shishkin Mesh ◽

Singularly Perturbed ◽

Convection Diffusion ◽

Small Parameters ◽

Perturbation Parameters ◽

Theoretical Results

AbstractA singularly perturbed convection-diffusion problem with two small parameters is considered. The problem is solved using the streamline-diffusion finite element method on a Shishkin mesh. We prove that the method is convergent independently of the perturbation parameters. Numerical experiments support these theoretical results.

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