Numerical solutions of kaup-kupershmidt and ıto equations with b-spline collocation method

Abstract

In this study, it is aimed to obtain the numerical solutions of two types of fifth-order Korteweg-de Vries (KdV) equations namely Kaup-Kupershmidt (K-K) and Ito. For this purpose, collocation finite element method is used. L2 and L error norms are computed for single soliton solutions to demonstrate the proficiency and accuracy of the present method. The method is shown to be unconditionally stable by performing the von-Neumann stability analysis.