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25-10-2019 | Original Paper | Issue 3/2020

An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems

Journal:: Numerical Algorithms > Issue 3/2020

Authors:: Mohammad Mehdizadeh Khalsaraei, Ali Shokri

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Abstract

In this paper, we present an explicit six-step singularly P-stable Obrechkoff method of tenth algebraic order for solving second-order linear periodic and oscillatory initial value problems of ordinary differential equations. The advantage of this new singularly P-stable Obrechkoff method is that it is a high-order explicit method, and thus does not require additional predictor stages. The numerical stability and phase properties of the new method is analyzed. Four numerical examples show that the new explicit method is more accurate than Obrechkoff schemes of the same order when applied to the numerical solution of second-order initial value problems with highly oscillatory solutions.

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Title: An explicit six-step singularly P-stable Obrechkoff method for the numerical solution of second-order oscillatory initial value problems
Authors:: Mohammad Mehdizadeh Khalsaraei
Ali Shokri
Publication date: 25-10-2019
DOI: https://doi.org/10.1007/s11075-019-00784-w
Publisher: Springer US
Journal: Numerical Algorithms
Issue 3/2020
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265

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