A class of singularly perturbed semilinear differential equations with interior layers

Farrell, P.; O’Riordan, E.; Shishkin, G.

doi:10.1090/S0025-5718-05-01764-3

A class of singularly perturbed semilinear differential equations with interior layers
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by P. A. Farrell, E. O’Riordan and G. I. Shishkin PDF

Math. Comp. 74 (2005), 1759-1776 Request permission

Abstract:

In this paper singularly perturbed semilinear differential equations with a discontinuous source term are examined. A numerical method is constructed for these problems which involves an appropriate piecewise-uniform mesh. The method is shown to be uniformly convergent with respect to the singular perturbation parameter. Numerical results are presented that validate the theoretical results.

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