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.
"A Galerkin Finite Element Method for Numerical Solutions of the Modified Regularized Long Wave Equation." Abstr. Appl. Anal. 2014 1 - 11, 2014. https://doi.org/10.1155/2014/438289