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

O’Riordan, E.; Pickett, M.; Shishkin, G.

doi:10.1090/S0025-5718-06-01846-1

Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems
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by E. O’Riordan, M. L. Pickett and G. I. Shishkin PDF

Math. Comp. 75 (2006), 1135-1154 Request permission

Abstract:

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.

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