Quintic B-spline Differential Quadrature for Burgers’ Equation

Abstract

In this study differential quadrature method based on quintic B-spline functions is setup for numerical solutions for nonlinear viscous Burgers’ equation. After space discretization with differential quadrature and application of boundary conditions, the resultant ordinary differential equation system is integrated in time by using Runge-Kutta method of order four. The method is validated by solving two initial value problems for the Burgers’ equation. The errors of the numerical solutions are measured by using discrete maximum norm. A comparison with some earlier works also given for the problem modeling fadeout of an initial shock.

Keywords

• quintic B-spline,Burgers’ Equation,differential quadrature method,shock wave,sinusoidal disturbance

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