Haar wavelet-based numerical investigation of coupled viscous Burgers' equation

Abstract

In this work, numerical solutions of the nonlinear coupled Burgers' equation with appropriate initial and boundary conditions in one space dimension are considered. A numerical method is proposed using the properties of uniform Haar wavelets together with a collocation method and based on semi-discretization along the space direction for solving a coupled viscous Burgers' equation. The semi-discretization scheme forms a system of nonlinear ordinary differential equations which is solved by the fourth-order Runge–Kutta method. Numerical experiments have been conducted in five examples to illustrate the merits of the proposed method. The relative errors $L_2$ and $L_{\mathrm{\infty }}$ are computed from obtained numerical results. It is shown that the proposed method is working well and produces satisfactory results.

Keywords:

• Haar wavelets
• discretization collocation scheme
• Runge–Kutta method
• coupled viscous Burgers' equation

2010 AMS Subject Classifications:

• 65Nxx
• 65N12
• 65N35
• 65T60
• 41A30

Acknowledgements

The authors thankfully acknowledge the comments of anonymous referees which improved the manuscript and are indebted to the editor for his illuminating advice and valuable discussion. Harpreet Kaur is thankful to Sant Longowal Institute of Engineering and Technology (SLIET), Longowal, India, for providing financial support as a senior research fellowship.