Solving a partially singularly perturbed initial value problem on Shishkin meshes

DOI10.1016/j.amc.2009.09.038zbMath1208.65099OpenAlexW1987212498MaRDI QIDQ846408

S. Valarmathi, P. Maragatha Meenakshi, John J. H. Miller

Publication date: 9 February 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.09.038

zbMATH Keywords

convergencenumerical resultssingular perturbationinitial value problemShishkin meshsystems of differential equationsinitial layerclassical finite difference schemefitted mesh

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

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• A parameter uniform numerical method for a system of singularly perturbed ordinary differential equations
• A numerical method for a system of singularly perturbed reaction-diffusion equations
• Approximation of the solutions of singularly perturbed boundary-value problems with a parabolic boundary layer
• A Parameter-Uniform Finite Difference Method for a Singularly Perturbed Initial Value Problem: a Special Case
• Methods of constructing grid approximations for singularly perturbed boundary-value problems. Condensing-grid methods