An optimal reproducing kernel method for linear nonlocal boundary value problems

Abstract

Based on the piecewise polynomial reproducing kernels, the authors presented the reproducing kernel method(RKM) for nonlocal boundary value problems. In this paper, we will present an optimal RKM for linear nonlocal boundary value problems by combining the piecewise polynomial kernel with polynomial kernel. The method is of high accuracy. Also, the method can avoid reducing the inhomogeneous boundary conditions to homogeneous boundary conditions and constructing reproducing kernel satisfying corresponding homogeneous boundary conditions. Numerical examples are included to demonstrate the validity of the new method.