Convergence of the sinc overlapping domain decomposition method (Q1294325)

An initial implementation of a sinc-collocation domain decomposition method for two-point boundary value problems with boundary singularities is investigated. The algorithm used to find the solution of an equation approximated with the overlapping method relies on the bordering algorithm [cf. \textit{H. B. Keller}, Numerical solution of bifurcation and nonlinear eigenvalue problems, in: Ph. H. Rabinowitz (ed.), Applications of bufurcation theory, Academic Press, New York, 359-384 (1977; Zbl 0581.65043)] and on block Gaussian elimination. The convergence proof of the overlapping sinc domain decomposition method for one-dimensional problems is presented. From the estimates for auxiliary problems, the sinc approximation is shown to converge to the solution of the ordinary differential equation.