Abstract

In this paper, the direct meshless local Petrov–Galerkin (DMLPG) approximation is proposed to solve the two-dimensional complex Ginzburg–Landau equation. DMLPG uses a generalized MLS (GMLS) method which directly approximates test functionals by values at nodes and therefore avoids integration over MLS shape functions and replaces it by a much cheaper integration over polynomials. An Implicit-Explicit method used to deal with the time derivative. Several examples are performed to compare the accuracy and efficiency of the DMLPG method with the traditional MLPG method.