Symmetric 2-Step 4-Point Hybrid Method for the Solution of General Third Order Differential Equations | OMICS International | Abstract
ISSN: 2168-9679

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## Symmetric 2-Step 4-Point Hybrid Method for the Solution of General Third Order Differential Equations

Kayode SJ and Obarhua FO*

Department of Mathematical Sciences, Federal University of Technology, Nigeria

*Corresponding Author:
Obarhua FO
Department of Mathematical Sciences
Federal University of Technology
P. M. B. 704, Akure, Nigeria
Tel: 234-8034540637
E-mail: [email protected]

Received Date: February 27, 2017; Accepted Date: April 21, 2017; Published Date: April 29, 2017

Citation: Kayode SJ, Obarhua FO (2017) Symmetric 2-Step 4-Point Hybrid Method for the Solution of General Third Order Differential Equations. J Appl Computat Math 6: 348. doi: 10.4172/2168-9679.1000348

Copyright: © 2017 Kayode SJ, et al. 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.

### Abstract

This research considers a symmetric hybrid continuous linear multistep method for the solution of general third order ordinary differential equations. The method is generated by interpolation and collocation approach using a combination of power series and exponential function as basis function. The approximate basis function is interpolated at both grid and off-grid points but the collocation of the differential function is only at the grid points. The derived method was found to be symmetric, consistent, zero stable and of order six with low error constant. Accuracy of the method was confirmed by implementing the method on linear and non-linear test problems. The results show better performance over known existing methods solved with the same third order problems. AMS 2010 Subject Classification: 65D05; 65L05; 65L06

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