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

Author

Listed:
  • 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
    Faculty of Mechanical and Industrial Engineering, Quchan University of Technology, Quchan 94771-77870, Iran)

  • Hamid Mohammad-Sedighi

    (Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz 61357-43337, Iran)

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.

Suggested Citation

  • Ali Shokri & Beny Neta & Mohammad Mehdizadeh Khalsaraei & Mohammad Mehdi Rashidi & Hamid Mohammad-Sedighi, 2021. "A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations," Mathematics, MDPI, vol. 9(8), pages 1-22, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:8:p:806-:d:532017
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