Compactly supported radial basis functions for solving certain high order partial differential equations in 3D

Compactly supported radial basis functions have been selected as basis functions for the derivation of closed-form particular solution in the process of solving certain high order partial differential equations in 3D. The method of particular solutions and the method of fundamental solutions are employed to numerically evaluate the particular solution and homogeneous solution of a 3D problem. Two numerical examples are given to demonstrate that the proposed method is applicable for handling large-scale problems.