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2017 Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations
Mohammad Alkasassbeh, Zurni Omar
J. Appl. Math. 2017: 1-8 (2017). DOI: 10.1155/2017/8510948

Abstract

A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.

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Mohammad Alkasassbeh. Zurni Omar. "Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations." J. Appl. Math. 2017 1 - 8, 2017. https://doi.org/10.1155/2017/8510948

Information

Received: 25 August 2016; Revised: 20 October 2016; Accepted: 23 October 2016; Published: 2017
First available in Project Euclid: 24 February 2017

zbMATH: 07037492
MathSciNet: MR3603379
Digital Object Identifier: 10.1155/2017/8510948

Rights: Copyright © 2017 Hindawi

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