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Keywords = singularly P-stable

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22 pages, 746 KiB  
Article
A Singularly P-Stable Multi-Derivative Predictor Method for the Numerical Solution of Second-Order Ordinary Differential Equations
by Ali Shokri, Beny Neta, Mohammad Mehdizadeh Khalsaraei, Mohammad Mehdi Rashidi and Hamid Mohammad-Sedighi
Mathematics 2021, 9(8), 806; https://doi.org/10.3390/math9080806 - 8 Apr 2021
Cited by 5 | Viewed by 2616
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, [...] Read more.
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. Full article
(This article belongs to the Special Issue Numerical Methods for Solving Differential Problems)
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