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A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers’ equation

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Abstract

In this paper, we investigate the numerical solutions of one dimensional modified Burgers’ equation with the help of Haar wavelet method. In the solution process, the time derivative is discretized by finite difference, the nonlinear term is linearized by a linearization technique and the spatial discretization is made by Haar wavelets. The proposed method has been tested by three test problems. The obtained numerical results are compared with the exact ones and those already exist in the literature. Also, the calculated numerical solutions are drawn graphically. Computer simulations show that the presented method is computationally cheap, fast, reliable and quite good even in the case of small number of grid points.

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Acknowledgments

We would like to thank the reviewers for their invaluable suggestions towards the improvement of the paper.

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Authors and Affiliations

  1. Department of Mathematics, İnonu University, Malatya, Turkey

    Ö. Oruç & A. Esen

  2. Department of Physics, İnonu University, Malatya, Turkey

    F. Bulut

Authors
  1. Ö. Oruç
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  2. F. Bulut
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  3. A. Esen
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Correspondence to F. Bulut.

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Oruç, Ö., Bulut, F. & Esen, A. A Haar wavelet-finite difference hybrid method for the numerical solution of the modified Burgers’ equation. J Math Chem 53, 1592–1607 (2015). https://doi.org/10.1007/s10910-015-0507-5

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  • DOI: https://doi.org/10.1007/s10910-015-0507-5

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