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Journals / Universal Journal of Mathematics and Applications / 2022 / Cilt: 5 - Sayı: 3

Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

Hefan YİN
Qi WANG
Pages
107–116
Publication Date
2022-09-30
DOI
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Finally, the conclusions are verified by several numerical experiments.

📌 3 Key Takeaways

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Objective & Hypothesis:The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients.
📊
Key Findings & Data:Firstly, the Runge-Kutta method is applied to the equation and the recurrence relationship of the numerical solution of the equation is obtained.
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Conclusion & Impact:Finally, the conclusions are verified by several numerical experiments.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Runge-Kutta methods · analytical stability · numerical stability

Abstract

The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients. Firstly, the Runge-Kutta method is applied to the equation and the recurrence relationship of the numerical solution of the equation is obtained. Secondly, it is proved that the Runge-Kutta method can preserve the convergence order. Thirdly, the stability conditions of the numerical solution under different matrix coefficients are given by Pad$\acute{e}$ approximation and order star theory. Finally, the conclusions are verified by several numerical experiments.

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Cite This Article

YİN, H., WANG, Q. (2022). Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients. Universal Journal of Mathematics and Applications, Cilt: 5 - Sayı: 3, 107–116. https://ajindex.com/articles/819895

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