A class of singularly perturbed quasilinear differential equations with interior layers

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

doi:10.1090/S0025-5718-08-02157-1

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

Math. Comp. 78 (2009), 103-127 Request permission

Abstract:

A class of singularly perturbed quasilinear differential equations with discontinuous data is examined. In general, interior layers will appear in the solutions of problems from this class. A numerical method is constructed for this problem class, which involves an appropriate piecewise-uniform mesh. The method is shown to be a parameter-uniform numerical method with respect to the singular perturbation parameter. Numerical results are presented, which support the theoretical results.

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