American Journal of Applied Sciences

Multistep Collocation Block Method for Direct Solution of Second Order Ordinary Differential Equations

John Olusola Kuboye and Zurni Omar

DOI : 10.3844/ajassp.2015.663.668

American Journal of Applied Sciences

Volume 12, Issue 9

Pages 663-668

Abstract

In this study, block method of order six for solving second order ordinary differential equations is developed. The method of interpolation of approximated power series and collocation of its second derivative is adopted in the derivation of the method. The developed method is applied in block form to produce approximate solution at five points simultaneously. The stability properties of the method such as order, error constants, consistency and convergence are investigated. The developed method was then applied to solve some initial value problems of second order ordinary differential equations and the numerical results indicated that the new method produced better accuracy than the existing methods when solving the same problems.

Copyright

© 2015 John Olusola Kuboye and Zurni Omar. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.