On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems

DOI10.1016/j.amc.2010.02.050zbMath1192.65118OpenAlexW2041773168MaRDI QIDQ972920

Carmelo Clavero, José Luis Gracia

Publication date: 21 May 2010

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

Full work available at URL: https://doi.org/10.1016/j.amc.2010.02.050

zbMATH Keywords

numerical resultsasymptotic behaviorsingular perturbationfinite difference methoduniform convergenceBakhvalov meshboundary layerShishkin meshbackward Euler methodspecial nonuniform meshparabolic reaction-diffusion problemssemidiscrete problemsVulanovic mesh

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50)

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Cites Work

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• A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions
• A uniformly convergent alternating direction HODIE finite difference scheme for 2D time-dependent convection-diffusion problems
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• -uniform schemes with high-order time-accuracy for parabolic singular perturbation problems
• Parameter uniform approximations for time‐dependent reaction‐diffusion problems
• A higher-order scheme for quasilinear boundary value problems with two small parameters

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