A differential quadrature method for numerical solutions of Burgers'‐type equations
International Journal of Numerical Methods for Heat & Fluid Flow
ISSN: 0961-5539
Article publication date: 14 September 2012
Abstract
Purpose
The purpose of this paper is to use the polynomial differential quadrature method (PDQM) to find the numerical solutions of some Burgers'‐type nonlinear partial differential equations.
Design/methodology/approach
The PDQM changed the nonlinear partial differential equations into a system of nonlinear ordinary differential equations (ODEs). The obtained system of ODEs is solved by Runge‐Kutta fourth order method.
Findings
Numerical results for the nonlinear evolution equations such as 1D Burgers', coupled Burgers', 2D Burgers' and system of 2D Burgers' equations are obtained by applying PDQM. The numerical results are found to be in good agreement with the exact solutions.
Originality/value
A comparison is made with those which are already available in the literature and the present numerical schemes are found give better solutions. The strong point of these schemes is that they are easy to apply, even in two‐dimensional nonlinear problems.
Keywords
Citation
Mittal, R.C. and Jiwari, R. (2012), "A differential quadrature method for numerical solutions of Burgers'‐type equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 7, pp. 880-895. https://doi.org/10.1108/09615531211255761
Publisher
:Emerald Group Publishing Limited
Copyright © 2012, Emerald Group Publishing Limited