The Method of Lines Solution of the Regularized Long-Wave Equation Using Runge-Kutta Time Discretization Method

A method of lines approach to the numerical solution of nonlinear wave equations typified by the regularized long wave (RLW) is presented. The method developed uses a finite differences discretization to the space. Solution of the resulting system was obtained by applying fourth Runge-Kutta time discretization method. Using Von Neumann stability analysis, it is shown that the proposed method is marginally stable. To test the accuracy of the method some numerical experiments on test problems are presented. Test problems including solitary wave motion, two-solitary wave interaction, and the temporal evaluation of a Maxwellian initial pulse are studied. The accuracy of the present method is tested with L∞ and L2 error norms and the conservation properties of mass, energy, and momentum under the RLW equation.