Quartic trigonometric B-spline algorithm for numerical solution of the regularized long wave equation

Abstract

In this paper, an application of the quartic trigonometric B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method based on the quartic trigonometric B-spline function in space discretization together with second and fourth order schemes in time discretization. The accuracy of the proposed methods are demonstrated by test problems and numerical results are compared with the exact solution and some previous results.

A new energy conservative scheme for regularized long wave equation

“…In [29], a collocation method depending on the cubic trigonometric B-spline approach based on a finite difference scheme was suggested to solve the modified RLW equation. In [15], [16], the B-spline Galerkin finite element space discretization with different time discretization was used to solve the RLW equation numerically. In [3], a numerical scheme for the equation was developed and analyzed by the Petrov-Galerkin method for the RLW equation in which the element shape functions are cubic and weight functions are quadratic B-splines.…”