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Reproducing Kernel Hilbert Space Method for Solving Bratu’s Problem

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Abstract

In this paper, we use the reproducing kernel Hilbert space method for solving a boundary value problem for the second order Bratu’s differential equation. Convergence analysis of presented method is discussed. The numerical approximations to the exact solution are computed and compared with other existing methods. Our presented method produces more accurate results in comparison with those obtained by Adomian decomposition, Laplace decomposition, B-spline, non-polynomial spline and Lie-group shooting methods. Our yardstick is absolute error. The comparison of the results with exact ones is made to confirm the validity and efficiency.

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Acknowledgments

The first and second authors acknowledge that this research supported by Firat University Scientific Research Projects Unit, Turkey is under the Research University Grant Scheme FF.12.09.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Fırat University, 23119, Elazig, Turkey

    Mustafa Inc

  2. Department of Mathematics, Faculty of Education, Dicle University, 21280, Diyarbakir, Turkey

    Ali Akgül

  3. Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, Heilongjiang, People’s Republic of China

    Fazhan Geng

Authors
  1. Mustafa Inc
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  2. Ali Akgül
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  3. Fazhan Geng
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Corresponding author

Correspondence to Mustafa Inc.

Additional information

Communicated by Ali Hassan Mohamed Murid.

This paper has been presented on the Symposium on Biomathematics and Ecology: Education and Research, November 9–11, 2012 by the second author. This paper is a part of PhD thesis of the second author.

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Inc, M., Akgül, A. & Geng, F. Reproducing Kernel Hilbert Space Method for Solving Bratu’s Problem. Bull. Malays. Math. Sci. Soc. 38, 271–287 (2015). https://doi.org/10.1007/s40840-014-0018-8

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  • DOI: https://doi.org/10.1007/s40840-014-0018-8

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