Modified Moving Least Square Collocation Method for Solving Wave Equations

Abstract

This paper presents a modified moving least square (MMLS) collocation method for solving wave equations. In contrast to the conventional moving least square (CMLS) method, this method modifies how discretization of computational points is done and decreases the number of base functions to simplify shape functions while solving high-dimensional problems. In addition, the proposed method maintains the independence of discretization for different dimensions, which is convenient to deal with computational domains in a simple manner while retaining a local character. The above improvement results in this approximation significantly saving calculation time while preserving accuracy of the solution. The numerical simulations show that MMLS collocation method has good stability and accuracy in analyzing high-dimensional wave propagation.