Fast and highly accurate reproducing kernels based approach for Poisson equation

In the existing papers, the reproducing kernel based approaches have been proposed to solve boundary value problems (BVPs) in ordinary differential equations (ODEs). However, it is difficult to extend these approaches to BVPs of partial differential equations due to the computational cost. In this letter, a new fast and highly accurate reproducing kernels based approach is proposed for Poisson equation. By eliminating the requirement to solve $N\times \tilde{N}$-dimensional linear systems, the present approach reduces the computational cost. The high accuracy of the present approach is confirmed by numerical simulation.