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Beckett, G.; Mackenzie, J. A.

On a uniformly accurate finite difference approximation of a singularly perturbed reaction-diffusion problem using grid equidistribution. (English) Zbl 0984.65076

J. Comput. Appl. Math. 131, No. 1-2, 381-405 (2001).
The authors consider the convergence of a finite difference scheme for a singularly perturbed reaction-diffusion boundary value problem using a nonuniform grid. Their analysis shows how the monitor function can be chosen to ensure that the accuracy of the numerical approximation is insensitive to the size of the singular perturbation parameter. The use of equidistribution principles appears in many practical grid adaption schemes. Numerical results are given that confirm the uniform convergence rates.
Reviewer: Qin Mengzhao (Beijing)

Cited in 1 Review
Cited in 57 Documents

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65L50 Mesh generation, refinement, and adaptive methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34E15 Singular perturbations for ordinary differential equations
35K57 Reaction-diffusion equations

Keywords:

uniform convergence; adaptivity; equidistribution; singular perturbation; reaction-diffusion equation; finite difference scheme; numerical results
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References:

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