TITLE:
Series and Exponentially-Fitted Two-Point Hybrid Method for General Second Order Ordinary Differential Equations
AUTHORS:
Sunday Jacob Kayode, Friday Oghenerukevwe Obarhua, Oluwatoyin Christiana Osuntope
KEYWORDS:
Exponentially-Fitted, Zero Stability, Hybrid Method, Symmetric, Error Constant, Basis Functions
JOURNAL NAME:
Open Access Library Journal,
Vol.10 No.8,
August
15,
2023
ABSTRACT: This article considered the development of a two-point hybrid method for the numerical solution of initial value problems of second order ordinary differential Equations (ODEs) using power series and exponentially-fitted basis function. Interpolation and collocation techniques were used to derive the method. The method was implemented in predictor-corrector mode. In order to increase the accuracy of the results of the method, the predictor was designed to have same order of accuracy as the corrector. The method is symmetric, consistent, zero-stable and has small error constant and has better accuracy over other methods in the reviewed literature when tested with some numerical examples.