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Numerical methods of fourth, sixth and eighth orders convergence for solving third order nonlinear ODEs

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  • Dang, Quang A.
  • Dang, Quang Long
  • Ngo, T. Kim Quy

Abstract

In this paper, we design numerical methods of fourth, sixth and eighth orders convergence for solving BVPs of fully third order nonlinear differential equations. The methods are based on the use of high order quadrature formulas for computing integrals containing Green function and its derivatives at each iteration of the iterative method on continuous level for finding the solutions of the BVPs. We prove that the order of the methods is equal to the order of quadrature methods used. Many examples confirm the theoretical conclusion.

Suggested Citation

  • Dang, Quang A. & Dang, Quang Long & Ngo, T. Kim Quy, 2024. "Numerical methods of fourth, sixth and eighth orders convergence for solving third order nonlinear ODEs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 397-414.
    • Handle: RePEc:eee:matcom:v:221:y:2024:i:c:p:397-414
    DOI: 10.1016/j.matcom.2024.03.018
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    References listed on IDEAS

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    1. Muhammad Aslam Noor & Eisa Al-Said & Khalida Inayat Noor, 2012. "Finite Difference Method for Solving a System of Third-Order Boundary Value Problems," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, April.
    2. Moghadam, Amin Abrishami & Soheili, Ali R. & Bagherzadeh, Amir Saboor, 2022. "Numerical solution of fourth-order BVPs by using Lidstone-collocation method," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    3. Costabile, F.A. & Gualtieri, M.I. & Napoli, A., 2021. "Lidstone-based collocation splines for odd-order BVPs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 186(C), pages 124-135.
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