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

Author

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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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