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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-04, Vol.9 (8), p.806
Main Authors: Shokri, Ali, Neta, Beny, Mehdizadeh Khalsaraei, Mohammad, Rashidi, Mohammad Mehdi, Mohammad-Sedighi, Hamid
Format: Article
Language:English
Subjects:
Algebra
Differential equations
linear multistep methods
Mathematics
Methods
multiderivative methods
Numerical analysis
Numerical integration
Ordinary differential equations
singularly P-stable
Stability
symmetric methods
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9080806