Solving second order ordinary differential equations by using Newton's interpolation and Aitken's methods


Mbagwu J. P. C. , Tunç C. , Enyoh C. E. , Onwuemekaa J. I.

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, vol.13, no.1, pp.1057-1066, 2022 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 13 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.22075/ijnaa.2021.24027.2657
  • Title of Journal : INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS
  • Page Numbers: pp.1057-1066
  • Keywords: Ordinary differential equations, Newton's interpolation method, Aitken's method

Abstract

In this paper, the methods called Newton's interpolation and Aitken's methods were developed and examined. We use Newton's interpolation and Aitken's methods to find the exact and analytic results for three different types of nonlinear ordinary differential equations (NLODEs) of first and second order through illustrative examples. By using the new method, we successfully handle some class of nonlinear ordinary differential equations of first and second order in a simple and elegant way compared to Newton's and Lagrange methods in previous studies. One can conclude that Newton's interpolation and Aitken's methods are easy to yield and implement actual precise results.