An efficient operational matrix approach for the solutions of Burgers' and fractional Burgers' equations using wavelets

Abstract

In this paper, we have developed an efficient Chebyshev wavelet-Picard method for solving Burgers’ equation and time-fractional Burgers’ equation. In order to get the solution, we decompose the nonlinear PDE by Picard method and then convert into a system of algebraic equations. Convergence analysis of the proposed wavelet method is also discussed. The proposed wavelet solutions are compared with the solutions obtained by Cole-Hopf transformation and Haar wavelet method. Satisfactory agreement with HAM and analytical solution is observed. Some illustrative examples are given to demonstrate the efficiency and accuracy of the proposed wavelet method.

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Acknowledgements

The authors are grateful to the Naval Research Board (Project No.:NRB447/SC/19-20) New Delhi for their financial support. We also acknowledge SASTRA Deemed University, Thanjavur for extending infrastructure support to carry out the study.

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Hariharan, G., Swaminathan, G. & Sripathy, B. An efficient operational matrix approach for the solutions of Burgers' and fractional Burgers' equations using wavelets. J Math Chem 59, 554–573 (2021). https://doi.org/10.1007/s10910-020-01206-2

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Keywords

  • Burgers’ equation
  • Time-fractional Burgers’ equation
  • Chebyshev wavelets
  • Hopf-Cole transformation
  • Operational matrices
  • Picard method