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

Ali Shokri, Beny Neta, Mohammad Mehdizadeh Khalsaraei, Mohammad Mehdi Rashidi and Hamid Mohammad-Sedighi
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Ali Shokri: Faculty of Mathematical Science, University of Maragheh, Maragheh 55181-83111, Iran
Beny Neta: Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA 93943, USA
Mohammad Mehdizadeh Khalsaraei: Faculty of Mathematical Science, University of Maragheh, Maragheh 55181-83111, Iran
Mohammad Mehdi Rashidi: Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu 610054, Sichuan, China
Hamid Mohammad-Sedighi: Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran

Mathematics, 2021, vol. 9, issue 8, 1-22

Abstract: 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.

Keywords: singularly P-stable; multiderivative methods; linear multistep methods; symmetric methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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