Higher Order Splitting Method for Numerical Solution Of Nonlinear Coupled System Viscous Burger's Equation

Year 2020, Volume: 8 Issue: 2, 234 - 243, 27.10.2020

Murat Yağmurlu , Yusuf Uçar , İhsan Çelikkaya

Abstract

In this study, the numerical solutions of nonlinear coupled system viscous Burgers equation with appropriate initial and boundary conditions are going to be obtained by Strang splitting method and also Ext4 and Ext6 methods obtained by extrapolation technique. To apply splitting methods, coupled system viscous Burgers equation split up into two subequation, one is linear and the other is nonlinear equation. Cubic B-spline functions and derivatives are used for the dependent variables u(x,t) and v(x,t) in each sub-equation obtained. Numerical schemas were obtained by applying each sub-equation of the collocation finite element method and the stability analyzes were investigated by the von-Neumann method. The effectiveness of the method was tested on three commonly used test problems in the literature. It was observed that the calculated numerical results were in agreement with the exact solution and compared with the previous studies.

Keywords

Operator Splitting method, Coupled viscous Burgers equation, Cubic B-spline functions, Collocation method, Strang splitting

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