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

Document Type : Research Paper

Authors

1 Department of Physics, Faculty of Physical Science, Imo State University, Owerri, Nigeria.

2 Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University 65080, Van-Turkey

3 Group Research in Analytical Chemistry, Environment and Climate Change (GRACE&CC), Department of Chemistry, Faculty of Physical Science, Imo State University, Owerri, Nigeria

10.22075/ijnaa.2021.24027.2657

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.

Keywords