A Parallel Boundary Value Technique for Singularly Perturbed Two-Point Boundary Value Problems

Authors:
J. Vigo-aguiar;S. Natesan
Affiliations:
Department of Applied Mathematics, University of Salamanca, E37008 Salamanca, Spain jvigo@usal.es;Department of Mathematics, Indian Institute of Technology, Guwahati-781039, India natesan@iitg.ernet.in
Venue:
The Journal of Supercomputing
Year:
2004

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Abstract

A class of singularly perturbed two-point boundary-value problems (BVPs) for second-order ordinary differential equations (DEs) is considered here. In order to obtain numerical solution to these problems, an iterative non-overlapping domain decomposition method is suggested. The BVPs are independent in each subdomain and one can use parallel computers to solve these BVPs. One of the characteristics of the method is that the number of processors available is a free parameter of the method. Practical experiments on a Silicon Graphics Origin 200, with 4 MIPS R10000 processors have been performed, showing the reliability and performance of the proposed parallel schemes. Error estimates for the solution and numerical examples are provided.