Numerical implementation for solving the symmetric regularized long wave equation

The paper presents a novel finite difference method for the symmetric regularized long wave equation. The time discretization is performed by using a four-level average difference technique for solving the fluid velocity independently from the density. At this stage, the numerical solution is easily solved by using the presented method since it does not require an extra effort to deal with a nonlinear term and the density. The existence and uniqueness of the numerical solution and the conservation of mass are guaranteed. The stability and convergence of the numerical solution with second-order accuracy on both space and time are also verified. Numerical results are carried out to confirm the accuracy of our theoretical results and the efficiency of the scheme. To illustrate the effectiveness and the advantage of the proposed method, the results at long-time behavior are compared with the ones obtained from previously known methods. Moreover, in the computation, the present method is applied to the collision of solitons under the effect of variable parameters.