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Math. Comput. Appl. 2016, 21(2), 12; doi:10.3390/mca21020012

Direct Solution of Second-Order Ordinary Differential Equation Using a Single-Step Hybrid Block Method of Order Five

Department of mathematics, College of Art and Sciences, Universiti Utara Sintok, Kedah 0060, Malaysia
These authors contributed equally to this work.
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Author to whom correspondence should be addressed.
Academic Editor: Mehmet Pakdemirli
Received: 1 February 2016 / Revised: 10 March 2016 / Accepted: 18 March 2016 / Published: 12 April 2016
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Abstract

This paper proposes a new hybrid block method of order five for solving second-order ordinary differential equations directly. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation is considered in deriving the method. Properties of the method such as zero stability, order, consistency, convergence and region of absolute stability are investigated. The new method is then applied to solve the system of second-order ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error. View Full-Text
Keywords: single-step; hybrid block method; system of second order ordinary differential equations; collocation and Interpolation method; direct solution single-step; hybrid block method; system of second order ordinary differential equations; collocation and Interpolation method; direct solution
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Abdelrahim, R.; Omar, Z. Direct Solution of Second-Order Ordinary Differential Equation Using a Single-Step Hybrid Block Method of Order Five. Math. Comput. Appl. 2016, 21, 12.

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