Numerical Algorithms for Direct Solution of Fourth Order Ordinary Differential Equations

Authors

  • J. O. Kuboye Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti, Nigeria
  • O. R. Elusakin Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti, Nigeria
  • O. F. Quadri Department of Mathematics, Federal University Oye-Ekiti, Oye-Ekiti, Nigeria

Keywords:

Interpolation, Collocation, Block methods, Fourth order, Ordinary differential equations

Abstract

This paper examines the derivation of hybrid numerical algorithms with step length(k) of five for solving fourth order initial value problems of ordinary differential equations directly. In developing the methods, interpolation and collocation techniques are considered. Approximated power series is used as interpolating polynomial and its fourth derivative as the collocating equation. These equations are solved using Gaussian-elimination approach in finding the unknown variables aj, j=0,...,10 which are substituted into basis function to give continuous implicit scheme. The discrete schemes and its derivatives that form the block are obtained
by evaluating continuous implicit scheme at non-interpolating points. The developed methods are of order seven and the results generated when the methods were applied to fourth order initial value problems compared favourably with existing methods.order initial value problems compared favourably with existing methods.

Dimensions

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Published

2020-11-15

How to Cite

Numerical Algorithms for Direct Solution of Fourth Order Ordinary Differential Equations. (2020). Journal of the Nigerian Society of Physical Sciences, 2(4), 218-227. https://doi.org/10.46481/jnsps.2020.100

Issue

Volume 2, Issue 4, November 2020

Section

Original Research
Copyright & Licensing

How to Cite

Numerical Algorithms for Direct Solution of Fourth Order Ordinary Differential Equations. (2020). Journal of the Nigerian Society of Physical Sciences, 2(4), 218-227. https://doi.org/10.46481/jnsps.2020.100