High Order Schemes for Reaction-Diffusion Singularly Perturbed Systems

DOI10.1007/978-3-642-00605-0_7zbMath1181.65104OpenAlexW223139005MaRDI QIDQ3653045

José Luis Gracia, Carmelo Clavero, Francisco Javier Lisbona

Publication date: 18 December 2009

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://zaguan.unizar.es/record/61328

zbMATH Keywords

linear systemsingular perturbationuniform convergencenumerical exampleserror boundsShishkin meshreaction-diffusion equationsnon-monotone finite difference scheme

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) 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)

Related Items (4)

An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems ⋮ An Asymptotic-Numerical Method for a Class of Weakly Coupled System of Singularly Perturbed Convection-Diffusion Equations ⋮ An almost fourth order uniformly convergent domain decomposition method for a coupled system of singularly perturbed reaction-diffusion equations ⋮ An almost third order finite difference scheme for singularly perturbed reaction-diffusion systems

Cites Work

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• A coupled system of singularly perturbed parabolic reaction-diffusion equations
• Maximum-norm error analysis of a non-monotone FEM for a singularly perturbed reaction-diffusion problem
• Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations
• High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems
• Layer-adapted meshes for a linear system of coupled singularly perturbed reaction-diffusion problems
• A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems
• A parameter robust numerical method for a two dimensional reaction-diffusion problem

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