A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation

Abstract EN

A Galerkin method for a modified regularized long wave equation is studied using finite elements in space, the Crank-Nicolson scheme, and the Runge-Kutta scheme in time.

In addition, an extrapolation technique is used to transform a nonlinear system into a linear system in order to improve the time accuracy of this method.

A Fourier stability analysis for the method is shown to be marginally stable.

Three invariants of motion are investigated.

Numerical experiments are presented to check the theoretical study of this method.