A differential quadrature method for numerical solutions of Burgers'‐type equations

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.

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