Collocation Method for the KdV-Burgers-Kuramoto Equation with Caputo Fractional Derivative

Abstract

The present article focuses on obtaining numerical solutions of time fractional KdV-Burger-Kuramoto equation (KBK) with the finite element collocation method. The finite element collocation methods are common and effective tool for solving nonlinear problems because of their reasonable computational costs. The idea underlying the method is seeking the numerical solutions in a form of a linear combination of unknown functions with basis at nodal points by avoid of integration. Thus, in this article, we achieve more accurate numerical results are obtained with the application of the method to KBK equation. Additionally, we show the efficiency and effectiveness of the method using comparisons of numerical results with exact solutions via error norms and their simulations.

Keywords

• KdV-Burger-Kuramoto equation,Collocation Finite Element Method,Quintic B-spline

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