New Efficient Numerical Model for Solving Second, Third and Fourth Order Ordinary Differential Equations Directly

Year 2020, Volume: 33 Issue: 4, 821 - 833, 01.12.2020

Bamikole Gbenga Ogunware , Olusola Ezekiel Aboların John Olusola Kuboye Emmanuel Oluseye Adeyefa

https://doi.org/10.35378/gujs.627677

Cited By: 4

Abstract

This article presents a two-step hybrid linear multistep
block method for solving second, third and fourth order initial value problems
of ordinary differential equations directly. The derivation of the method was
done using collocation and interpolation techniques while approximated power
series was used as an interpolating polynomial. The fourth derivative of the
power series is collocated at the entire grid and off grid points while the
fifth and sixth derivatives of the polynomial are collocated at the end point
only. The basic properties of the developed method, that is, order, error
constant, zero stability, region of absolute stability, convergence and
consistence of the method are properly investigated. The numerical results
demonstrated that the scheme developed handles second, third and fourth order
ordinary differential equations efficiently and also better in accuracy when
compared with existing methods. The proposed method takes away the burden of
developing separate method for the solution of second, third and fourth order
initial value problem of ordinary differential equations. 

Keywords

Hybrid Block Method, Collocation, , interpolation, Higher Order Ordinary Differential Equations, Power Series

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