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Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate

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Abstract

We present a new approach depending on reproducing kernel method (RKM) for time-fractional Kawahara equation with variable coefficient. This approach consists of obtaining an orthonormal basis function on specific Hilbert spaces. In this regard, some special Hilbert spaces are defined. Kernel functions of these special spaces are given and basis functions are obtained. The approximate solution is attained as serial form. Convergence analysis, error estimation and stability analysis are presented after obtaining the approximate solution. To show the power and effect of the method, two examples are solved and the results are given as table and graphics. The results demonstrate that the presented method is very efficient and convenient for Kawahara equation with fractional order.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey

    Onur Saldır & Mehmet Giyas Sakar

  2. Department of Statistics, Faculty of Sciences, Van Yuzuncu Yil University, 65080, Van, Turkey

    Fevzi Erdogan

Authors
  1. Onur Saldır
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  2. Mehmet Giyas Sakar
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  3. Fevzi Erdogan
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Correspondence to Onur Saldır.

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Communicated by José Tenreiro Machado.

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Saldır, O., Sakar, M.G. & Erdogan, F. Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate. Comp. Appl. Math. 38, 198 (2019). https://doi.org/10.1007/s40314-019-0979-1

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  • DOI: https://doi.org/10.1007/s40314-019-0979-1

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