Numerical simulation of two dimensional quasilinear hyperbolic equations by polynomial differential quadrature method

Abstract

Purpose

The purpose of this paper is to propose a numerical technique based on polynomial differential quadrature method (PDQM) to find the numerical solutions of two-space-dimensional quasilinear hyperbolic partial differential equations subject to appropriate Dirichlet and Neumann boundary conditions.

Design/methodology/approach

The PDQM reduced the equations into a system of second order linear differential equation. The obtained system is solved by RK4 method by converting into a system of first ordinary differential equations.

Findings

The accuracy of the proposed method is demonstrated by several test examples. The numerical results are found to be in good agreement with the exact solutions. The proposed technique can be applied easily for multidimensional problems.

Originality/value

The main advantage of the present scheme is that the scheme gives very accurate and similar results to the exact solutions by choosing less number of grid points and the problem can be solved up to big time. The good thing of the present technique is that it is easy to apply and gives us better accuracy in less numbers of grid points as comparison to the other numerical techniques.

Citation

Kumar, V., Jiwari, R. and Kumar Gupta, R. (2013), "Numerical simulation of two dimensional quasilinear hyperbolic equations by polynomial differential quadrature method", Engineering Computations, Vol. 30 No. 7, pp. 892-909. https://doi.org/10.1108/EC-02-2012-0030