Numerical Solution of Modified Forms of Camassa-Holm and Degasperis-Procesi Equations via Quartic B-Spline Collocation Method

Abstract

In this paper, a collocation finite difference scheme based on Quartic B-spline function is developed for solving non-linear modified Camassa-Holm and Degasperis-Procesi equations. A finite difference scheme and Quartic B-spline function are used to discretize the time and spatial derivatives, respectively. The obtained numerical results are compared with the exact analytical solutions and some methods existing in literature. The numerical solutions of proposed non-linear equations are acquired without any linearization technique. The convergence of the method is proved of order \((\Delta t + h^2)\). The efficiency of the proposed scheme is demonstrated through illustrative examples. The presented scheme is realized to be a very reliable alternate method to some existing schemes for such physical problems.