A novel Gaussian-cubic-based backward substitution method using symmetric variable shape parameter

Abstract

In this paper, we make the first attempt to apply the Gaussian-cubic basis function in the novel backward substitution method for solving linear and nonlinear problems in irregular domains. To improve the solution accuracy, the weighted parameters of the provided hybrid kernel are varying instead of constant ones in traditional methods. The shape parameters are determined by a symmetric variable shape parameter scheme. Furthermore, a counterintuitive ghost-points method is employed as the strategy for placing the center nodes in the basis functions. To evaluate the accuracy and efficiency of the proposed method, several 2D and 3D numerical examples are considered and the numerical results are compared with the traditional backward substitution method and the results in references. And the method can be used to solve nonlinear problems with some linearization techniques. The superior accuracy and efficiency have been validated.