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An efficient numerical algorithm based on Haar wavelet for solving a class of linear and nonlinear nonlocal boundary-value problems

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Abstract

Based on Haar wavelet a new numerical method for the solution of a class of nth-order boundary-value problems (BVPs) with nonlocal boundary conditions is proposed. This new method is an extension of the Haar wavelet method (Siraj-ul-Islam et al. in Math Comput Model 50:1577–1590, 2010; Int J Therm Sci 50:686–697, 2011) from BVPs with local boundary conditions to BVPs with a class of nonlocal boundary conditions. A major advantage of the proposed method is that it is applicable to both linear and nonlinear BVPs. The method is tested on BVPs of third- and fourth-order. The numerical results are compared with an existing method in the literature and analytical solutions. The numerical experiments demonstrate the accuracy and efficiency of the proposed method.

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Authors and Affiliations

  1. Department of Mathematics, University of Peshawar, Peshawar, Pakistan

    Imran Aziz & Muhammad Nisar

  2. Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan

    Siraj-ul-Islam

Authors
  1. Imran Aziz
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  2. Siraj-ul-Islam
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  3. Muhammad Nisar
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Correspondence to Imran Aziz.

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Aziz, I., Siraj-ul-Islam & Nisar, M. An efficient numerical algorithm based on Haar wavelet for solving a class of linear and nonlinear nonlocal boundary-value problems. Calcolo 53, 621–633 (2016). https://doi.org/10.1007/s10092-015-0165-9

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  • DOI: https://doi.org/10.1007/s10092-015-0165-9

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