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An Approximation Method for Solving Burgers’ Equation Using Legendre Wavelets

  • S. G. VenkateshEmail author
  • S. K. Ayyaswamy
  • S. Raja Balachandar
Research Article

Abstract

In this paper, we study the solution of the Burgers’ equation, a non-linear Partial Differential equation, using Legendre wavelets based technique. Burgers’ equation is an essential partial differential equation from fluid mechanics and is also used extensively in other areas of engineering such as gas dynamics, traffic flow modeling, acoustic wave propagation, and so on. The method is based on the function approximation so that that the connection coefficients can be identified easily and the series is the approximate solution or in closed form is the exact solution. Illustrative examples have been demonstrated to promote validity and applicability of the proposed method.

Keywords

Burgers’ equation Legendre polynomials Legendre wavelets Legendre wavelet method Approximation methods Convergence analysis 

Notes

Acknowledgement

The authors wish to thank Department of Science and Technology, Government of India for the financial sanction towards this work under FIST Programme SR\FST\MSI-107/2015.

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Copyright information

© The National Academy of Sciences, India 2017

Authors and Affiliations

  • S. G. Venkatesh
    • 1
    Email author
  • S. K. Ayyaswamy
    • 1
  • S. Raja Balachandar
    • 1
  1. 1.Department of Mathematics, School of Humanities and SciencesSASTRA UniversityThanjavurIndia

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