A novel meshless space-time backward substitution method and its application to nonhomogeneous advection-diffusion problems

Abstract

For time-dependent problems, a novel space-time backward substitution method is proposed in this paper. By employing the space-time radial basis function and the space-time trigonometric basis function in the original backward substitution method, the space-time backward substitution method is obtained. Compared with the traditional backward substitution method, this novel numerical method avoids the time-difference measurement in the temporal approximation, which may result in accumulative errors, and at the same time maintains the existing advantages. Furthermore, the proposed method can be easily used to solve more general time-dependent problems. To evaluate the accuracy and efficiency, several numerical examples are tested and compared.