A NOVEL SCHEME BASED ON COLLOCATION FINITE ELEMENT METHOD TO GENERALISED OSKOLKOV EQUATION

Abstract

This article is concerned with designing numerical schemes for the generalised Oskolkov equation using the quintic B-spline collocation finite element method. Applying the von-Neumann theory, it is shown that the proposed method is marginally unconditionally stable. It was obtained the theoretical bound of the error in the full discrete scheme for the first time in the literature. The accuracy and effectiveness of the method checked with three model problems, consisting of a single solitary wave, Gaussian initial condition and growth of an undular bore. The performance of the new method is demonstrated by calculating invariant I and error norms L2 and L∞. Results are displayed both numerically and graphically. Numerical experiments support the correctness and robustness of the method which can be further used for solving such problems.