Parallel implementation of a spline based computational approach for singular perturbation problems

Abstract

In this paper, a parallelizable computational technique for singularly perturbed reaction-diffusion problems is analyzed and implemented on parallel computer. In this technique, the domain is decomposed into non-overlapping subdomains, and boundary value problems are posed on each subdomain with suitable boundary conditions. Then, each problem is solved by the adaptive spline based difference scheme on each subinterval on parallel computer. Detailed theoretical analysis is provided to prove the convergence of the technique. To check the validity of the method, parallel implementation is performed on a numerical example and results are presented. © 2006 Springer-Verlag.