The interpolating element-free Galerkin method for solving Korteweg–de Vries–Rosenau-regularized long-wave equation with error analysis

Abstract

The main target of this investigation is to develop a new numerical method for solving a class of wave models, i.e., the Korteweg–de Vries–Rosenau-regularized long-wave equation with application in plasma physics. The developed technique is concerning the interpolating element-free Galerkin method. The test and trial functions for the interpolating element-free Galerkin technique have been chosen from the interpolating moving least squares approximation. The interpolating moving least squares approximation shape functions unlike the moving least squares shape functions have the delta Kronecker property due to the use of a singular weight function. The stability and convergence of the new scheme are analyzed. Furthermore, the existence and uniqueness of solution have been proved for the full-discrete scheme. Finally, several examples in one- and two-dimensional cases have been studied to confirm the influence of the new scheme.