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.
Mathematics of Computation
First published in Mathematics of Computation in 2009, published by the American Mathematical Society.
Farrell, Paul A; O'Riordan, Eugene; Shishkin, Grigori I (2009). A Class of Singularly Perturbed Quasilinear Differential Equations with Interior Layers. Mathematics of Computation 78(265) 103-127. Retrieved from https://oaks.kent.edu/cspubs/10