Abstract
An orthogonal spline collocation method with C1 splines of degree on a Shishkin mesh is formulated and analyzed for the approximate solution of a singularly perturbed semilinear reaction diffusion problem. A convergence analysis yields parameter uniform error estimates of order
in an L2 discrete norm and of order
in weighted Hm norms, m = 1, 2, where N is the number of mesh subintervals. Results of numerical experiments support the analytical results, and also exhibit parameter uniform error estimates in other norms for which an analysis has yet to be derived.
Acknowledgments
The authors thank Prof. Amiya Pani, IIT Bombay, for his valuable comments and suggestions. Support was received by GF from IIT Bombay while a Distinguished Guest Professor at that institution.
Disclosure statement
No potential conflict of interest was reported by the authors.