The Schwarz alternating sinc domain decomposition method

Abstract

The overlapping sinc-collocation domain decomposition method combined with the Schwarz alternating technique is developed for two-point boundary-value problems for second-order ordinary differential equations with singularities. The discrete system is formulated and the solution technique is described. It is shown that this method has an exponential convergence rate even in the presence of singularities. The details of the convergence proof are given for a sinc-collocation method applied to second-order, two-point boundary-value problems when the original domain is divided into two subdomains. The extension to multiple domains is then straightforward. The analytical results are illustrated with a numerical example that exhibits the exponential convergence rate.