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Open AccessArticle

A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations

1
Faculty of Mathematical Science, University of Maragheh, Maragheh 55181-83111, Iran
2
Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
3
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, China
4
Faculty of Mechanical and Industrial Engineering, Quchan University of Technology, Quchan 94771-77870, Iran
5
Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran
*
Author to whom correspondence should be addressed.
Academic Editor: Mehdi Salimi
Mathematics 2021, 9(8), 806; https://doi.org/10.3390/math9080806
Received: 20 February 2021 / Revised: 20 March 2021 / Accepted: 27 March 2021 / Published: 8 April 2021
(This article belongs to the Special Issue Numerical Methods for Solving Differential Problems)
In this paper, a symmetric eight-step predictor method (explicit) of 10th order is presented for the numerical integration of IVPs of second-order ordinary differential equations. This scheme has variable coefficients and can be used as a predictor stage for other implicit schemes. First, we showed the singular P-stability property of the new method, both algebraically and by plotting the stability region. Then, having applied it to well-known problems like Mathieu equation, we showed the advantage of the proposed method in terms of efficiency and consistency over other methods with the same order. View Full-Text
Keywords: singularly P-stable; multiderivative methods; linear multistep methods; symmetric methods singularly P-stable; multiderivative methods; linear multistep methods; symmetric methods
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MDPI and ACS Style

Shokri, A.; Neta, B.; Mehdizadeh Khalsaraei, M.; Rashidi, M.M.; Mohammad-Sedighi, H. A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations. Mathematics 2021, 9, 806. https://doi.org/10.3390/math9080806

AMA Style

Shokri A, Neta B, Mehdizadeh Khalsaraei M, Rashidi MM, Mohammad-Sedighi H. A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations. Mathematics. 2021; 9(8):806. https://doi.org/10.3390/math9080806

Chicago/Turabian Style

Shokri, Ali; Neta, Beny; Mehdizadeh Khalsaraei, Mohammad; Rashidi, Mohammad M.; Mohammad-Sedighi, Hamid. 2021. "A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations" Mathematics 9, no. 8: 806. https://doi.org/10.3390/math9080806

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