Convergence of the sinc overlapping domain decomposition method

The sinc-collocation overlapping method is developed for two-point boundary-value problems for second-order ordinary differential equations. The discrete system is formulated and the bordering algorithm used for the solution of this system is described. It is then shown that the convergence rate is exponential even if the solution has boundary singularities. The details of the convergence proof are given for a sinc-collocation method for 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 numerical examples that exhibit the exponential convergence rate.