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Efficient Numerical Scheme for the Solution of Tenth Order Boundary Value Problems by the Haar Wavelet Method

Author

Listed:
  • Rohul Amin

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • Kamal Shah

    (Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa 18000, Pakistan)

  • Imran Khan

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • Muhammad Asif

    (Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa 25120, Pakistan)

  • Mehdi Salimi

    (Department of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1, Canada
    Center for Dynamics, Faculty of Mathematics, Technische Universität Dresden, 01062 Dresden, Germany)

  • Ali Ahmadian

    (Institute of IR 4.0, The National University of Malaysia (UKM), Bangi 43600, Malaysia)

Abstract

In this paper, an accurate and fast algorithm is developed for the solution of tenth order boundary value problems. The Haar wavelet collocation method is applied to both linear and nonlinear boundary value problems. In this technqiue, the tenth order derivative in boundary value problem is approximated using Haar functions and the process of integration is used to obtain the expression of lower order derivatives and approximate solution for the unknown function. Three linear and two nonlinear examples are taken from literature for checking validation and the convergence of the proposed technique. The maximum absolute and root mean square errors are compared with the exact solution at different collocation and Gauss points. The experimental rate of convergence using different number of collocation points is also calculated, which is nearly equal to 2.

Suggested Citation

  • Rohul Amin & Kamal Shah & Imran Khan & Muhammad Asif & Mehdi Salimi & Ali Ahmadian, 2020. "Efficient Numerical Scheme for the Solution of Tenth Order Boundary Value Problems by the Haar Wavelet Method," Mathematics, MDPI, vol. 8(11), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1874-:d:436599
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    References listed on IDEAS

    as
    1. Shahid S. Siddiqi & Muzammal Iftikhar, 2013. "Numerical Solution of Higher Order Boundary Value Problems," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, April.
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