Numerical Solutions of Symmetric Regularized Long Wave Equations Using Collocation of Cubic B-splines Finite Element

In this work, we present a new methodology to obtain numerical solutions of symmetric regularized long wave equations. Our approach is based on collocation of modified cubic B-spline basis functions over the finite elements. First, we discretize the given equation in space and then we use collocation of modified cubic B-spline basis functions for unknown dependent variables u, v and their derivatives w.r.t. space variable x, which produces a system of first-order ordinary differential equations. This system of differential equations has been solved by SSP-RK54 scheme. The stability of the method has been discussed and shown that it is unconditionally stable. The efficiency of the proposed method has been confirmed with numerical experiments, which shows that the obtained results are acceptable and are in good agreement with earlier studies. Ease of implementation and very small size of computational work are two major advantages of this approach. Moreover, this method provides approximate solutions not only at the grid points, but also at any point in the solution range.