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

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

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 221, issue C, 397-414

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.

Keywords: Third order nonlinear differential equation; Euler–Maclaurin expansion; Iterative methods; High order numerical methods (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:221:y:2024:i:c:p:397-414

DOI: 10.1016/j.matcom.2024.03.018

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