Different Implementation Approaches of the Strong Form Meshless Implementation of Taylor Series Method

Abstract

Based on the Taylor series expansion (TSE) and employing the technique of differential transform method (DTM), three new meshless approaches which are called Meshless Implementation of Taylor Series Methods (MITSM) are presented. In particular, Strong Form Meshless Implementation of Taylor Series Methods (SMITSM) are studied in this paper. Then, the basis functions are used to solve a 1D second-order ordinary differential equation and 2D Laplace equation by using the SMITSM. Comparisons are made with the analytical solutions and results of Symmetric Smoothed Particle Hydrodynamics (SSPH) method. We also compared the effectiveness of the SMITSM and SSPH method by considering various particle distributions, nonhomogeneous terms and number of terms in the basis functions. It is observed that the MITSM has the conventional convergence properties and, at the expense of CPU time, yields smaller L2 error norms than the SSPH method, especially in the existence of nonsmooth nonhomogeneous problems.