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Dergiler / Fundamental Journal of Mathematics and Applications / 2026 / Volume: 4 Issue: 3

Dynamic Behavior of Euler-Maclaurin Methods for Differential Equations with Piecewise Constant Arguments of Advanced and Retarded Type

Hefan Yin(Guangdong University of Technology)0000-0001-7182-3272
Qi Wang(Guangdong University of Technology)0000-0003-3578-2551
Sayfa
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Yayın Tarihi
2021-09-30
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Finally, several numerical examples confirm the corresponding conclusions.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The paper deals with three dynamic properties of the numerical solution for differential equations with piecewise constant arguments of advanced and retarded type: oscillation, stability and convergence.
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Temel Bulgular & Veri:It is proved that the convergence order of numerical method is 2n+2.
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Sonuç & Katkı:Finally, several numerical examples confirm the corresponding conclusions.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Euler-Maclaurin methods · numerical solution · oscillation

Abstract

The paper deals with three dynamic properties of the numerical solution for differential equations with piecewise constant arguments of advanced and retarded type: oscillation, stability and convergence. The Euler-Maclaurin methods are used to discretize the equations. According to the characteristic theory of the difference equation, the oscillation and stability conditions of the numerical solution are obtained. It is proved that the convergence order of numerical method is 2n+2. Furthermore, the relationship between stability and oscillation is discussed for analytic solution and numerical solution, respectively. Finally, several numerical examples confirm the corresponding conclusions.

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Bu Makaleye Atıf Yap

Yin, H., Wang, Q. (2021). Dynamic Behavior of Euler-Maclaurin Methods for Differential Equations with Piecewise Constant Arguments of Advanced and Retarded Type. Fundamental Journal of Mathematics and Applications, Volume: 4 Issue: 3. https://doi.org/10.33401/fujma.906230

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