Numerical Investigation of Modified Fornberg Whitham Equation

Abstract

The aim of this study is to obtain numerical solutions of the modified Fornberg Whitham equation via collocation finite element method combined with operator splitting method. The splitting method is used to convert the original equation into two sub equations including linear and nonlinear part of the equation as a slight modification of splitting idea. After splitting progress, collocation method is used to reduce the sub equations into algebraic equation systems. For this purpose, quintic B-spline base functions are used as a polynomial approximation for the solution. The effectiveness and efficiency of the method and accuracy of the results are measured with the error norms $L_{2}$ and $L_{\infty}$. The presentations of the numerical results are shown by graphics as well.