Analyzing modified equal width (MEW) wave equation using the improved element-free Galerkin method

Abstract

Abstract The element-free Galerkin (EFG) method is a promising method for solving partial differential equations in which trial and test functions employed in the discretization process result from moving least-squares (MLS) approximation. In this paper, by employing the improved moving least-squares (IMLS) approximation, we derive formulae for an improved element-free Galerkin (IEFG) method for the modified equal width (MEW) wave equation. A variation of the method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are fewer coefficients in the IMLS approximation than in the MLS approximation and in the IEFG method, fewer nodes are selected in the entire domain than in the conventional EFG method. Therefore, the IEFG method may result a better computing speed. In this paper, the effectiveness of the IEFG method for modified equal width (MEW) wave equation is investigated by numerical examples.