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.
Mathematics of Computation
First published in Mathematics of Computation in 2005, published by the American Mathematical Society.
Farrell, Paul A; O'Riordan, Eugene; Shishkin, Grigori I (2005). A Class of Singularly Perturbed Semilinear Differential Equations with Interior Layers. Mathematics of Computation 74(252) 1759-1776. Retrieved from https://oaks.kent.edu/cspubs/11