Boundary reduction technique and rational Sinc domain decomposition method

Sinc method is widely used for solving the boundary value problems because of the ease with which it may handle the presence of singularities or unbounded domains. In this paper, the domain decomposition method is used to deal with problems with interior layers and problems posed on irregular domains. With boundary reduction technique, the functional values on internal points can be eliminated. The scheme is based on a direct approach based on the corresponding compatibility matching conditions between sub-domains. Numerical experiments show that rational Sinc domain decomposition method based on the interpolation of the highest derivatives (RSIHD-DDM) is effective for treating problems with interior layers or boundary layers on irregular domains.