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Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets

Sapna Pandit (Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India)
Manoj Kumar (Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, India)
R.N. Mohapatra (Department of Mathematics, University of Central Florida, Orlando, Florida, USA)
Ali Saleh Alshomrani (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 7 August 2017

Abstract

Purpose

This paper aims to find the numerical solution of planar and non-planar Burgers’ equation and analysis of the shock behave.

Design/methodology/approach

First, the authors discritize the time-dependent term using Crank–Nicholson finite difference approximation and use quasilinearization to linearize the nonlinear term then apply Scale-2 Haar wavelets for space integration. After applying this scheme on partial differential, the equation transforms into a system of algebraic equation. Then, the system of equation is solved using Gauss elimination method.

Findings

Present method is the extension of the method (Jiwari, 2012). The numerical solutions using Scale-2 Haar wavelets prove that the proposed method is reliable for planar and non-planar nonlinear Burgers’ equation and yields results better than other methods and compatible with the exact solutions.

Originality/value

The numerical results for non-planar Burgers’ equation are very sparse. In the present paper, the authors identify where the shock wave and discontinuity occur in planar and non-planar Burgers’' equation.

Keywords

Acknowledgements

The authors express their sincere gratitude to the anonymous reviewers and editors for their valuable suggestions toward the improvement of the paper.

Citation

Pandit, S., Kumar, M., Mohapatra, R.N. and Alshomrani, A.S. (2017), "Shock waves analysis of planar and non planar nonlinear Burgers’ equation using Scale-2 Haar wavelets", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 27 No. 8, pp. 1814-1850. https://doi.org/10.1108/HFF-05-2016-0188

Publisher

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Emerald Publishing Limited

Copyright © 2017, Emerald Publishing Limited