Numerical stability and oscillation of the Runge-Kutta methods for equation \(x'(t)=ax(t)+a_0x(M[\frac{t+N}{M}])\)

DOI10.1186/1687-1847-2012-146zbMath1416.65210OpenAlexW1989636858WikidataQ59289834 ScholiaQ59289834MaRDI QIDQ320438

Minghui Song, Ming-Zhu Liu

Publication date: 6 October 2016

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1847-2012-146

zbMATH Keywords

stabilityoscillationdifferential equationRunge-Kutta method

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

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Uses Software

• RODAS

Cites Work

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• Oscillation analysis of numerical solution in the \(\theta\)-methods for equation \(x\prime (t) + ax(t) + a_{1}x([t - 1) = 0\)]
• Numerical methods for impulsive differential equation
• Differential equations alternately of retarded and advanced type
• Stability of Runge--Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0}u([t)\).]
• Stability of Runge-Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0} u([t)+a_{1} u([t-1])\)]
• Stability of \(\theta\)-methods for advanced differential equations with piecewise continuous arguments
• Solving Ordinary Differential Equations I
• An Equation Alternately of Retarded and Advanced Type
• Order stars and stability theorems

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