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Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method

Author

Listed:
  • Mart Ratas

    (Deptartment of Cybernetics, School of Science, Tallinn University of Technology, 12616 Tallinn, Estonia)

  • Jüri Majak

    (Deptartment of Mechanical and Industrial Engineering, School of Engineering, Tallinn University of Technology, 12616 Tallinn, Estonia)

  • Andrus Salupere

    (Deptartment of Cybernetics, School of Science, Tallinn University of Technology, 12616 Tallinn, Estonia)

Abstract

The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed.

Suggested Citation

  • Mart Ratas & Jüri Majak & Andrus Salupere, 2021. "Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method," Mathematics, MDPI, vol. 9(21), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2809-:d:672604
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    References listed on IDEAS

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    7. Nazir, Shah & Shahzad, Sara & Wirza, Rahmita & Amin, Rohul & Ahsan, Muhammad & Mukhtar, Neelam & García-Magariño, Iván & Lloret, Jaime, 2019. "Birthmark based identification of software piracy using Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 144-154.
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    Cited by:

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