Strong form meshless implementation of Taylor series method

A new meshless approach is investigated by using Taylor series expansion and technique of differential transform method, which is called Meshless Implementation of Taylor Series Method (MITSM). In particular, Strong form Meshless Implementation of Taylor Series Method (SMITSM) is 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.