Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems

In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomp...

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Bibliographic Details
Published in:Mathematics of computation 2006-07, Vol.75 (255), p.1135-1154
Main Authors: E. O'Riordan, M. L. Pickett, G. I. Shishkin
Format: Article
Language:English
Subjects:
Approximation
Boundary conditions
Boundary layers
Error bounds
Error rates
Minimum principle
Numerical methods
Transition points
Truncation errors
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Summary:In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind finite difference operator and an appropriate piecewise uniform mesh is constructed. Parameter-uniform error bounds for the numerical approximations are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.
ISSN:0025-5718
1088-6842
DOI:10.1090/S0025-5718-06-01846-1