An almost fourth-order parameter-robust numerical method for a linear system of \((M \geq 2)\) coupled singularly perturbed reaction-diffusion problems (Q2865631)
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scientific article; zbMATH DE number 6235023
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An almost fourth-order parameter-robust numerical method for a linear system of \((M \geq 2)\) coupled singularly perturbed reaction-diffusion problems |
scientific article; zbMATH DE number 6235023 |
Statements
2 December 2013
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parameter-robust convergence
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system of linear coupled reaction-diffusion problems
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generalized Shishkin mesh
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fourth-order compact difference scheme
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central difference scheme
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singular perturbation
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numerical example
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An almost fourth-order parameter-robust numerical method for a linear system of \((M \geq 2)\) coupled singularly perturbed reaction-diffusion problems (English)
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We investigate an almost fourth-order parameter-robust numerical method for a linear system of (\(M \geq 2)\) coupled singularly perturbed reaction-diffusion problems. A priori bounds on the solution and its derivatives are given, and a higher-order decomposition of the exact solution into its regular and layer parts is constructed. A higher-order finite difference scheme which is a suitable combination of the fourth-order compact difference scheme and the standard central difference scheme is described on a generalized Shishkin mesh. Numerical examples are given to validate the theoretical results discussed.
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