Numerical treatment for Burgers–Fisher and generalized Burgers–Fisher equations

Abstract

In this paper, the discontinuous Legendre wavelet Galerkin method is proposed for the numerical solution of the Burgers–Fisher and generalized Burgers–Fisher equations. This method combines both the discontinuous Galerkin and the Legendre wavelet Galerkin methods. Various properties of Legendre wavelets have been used to find the variational form of the governing equation. This variational form transforms it into a system of ordinary differential equations which will be solved numerically. Some illustrative examples are presented to emphasize the efficiency and reliability of the proposed method.

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Acknowledgements

It is not out of place to mention that the author is deeply indebted to respected eminent professor Dr. A. M. Wazwaz of Saint Xavier University, Chicago, USA, for sparing his valuable time in reading the paper carefully for refinement of literature as well as grammatical corrections.

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Correspondence to S. Saha Ray.

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Kumar, S., Saha Ray, S. Numerical treatment for Burgers–Fisher and generalized Burgers–Fisher equations. Math Sci (2020). https://doi.org/10.1007/s40096-020-00356-3

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Keywords

  • Burgers–Fisher equation
  • Legendre wavelets
  • Operational matrix for derivative
  • Variational Form