Numerical stability and oscillation of the Runge-Kutta methods for the differential equations with piecewise continuous arguments alternately of retarded and advanced type

DOI10.1186/1029-242X-2012-290zbMath1280.65070OpenAlexW2117401754WikidataQ59290954 ScholiaQ59290954MaRDI QIDQ388065

Minghui Song, Ming-Zhu Liu

Publication date: 18 December 2013

Published in: Journal of Inequalities and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1029-242x-2012-290

zbMATH Keywords

stabilityoscillationnumerical experimentsdelay differential equationRunge-Kutta methodsanalytic stability regionpiecewise continuous arguments

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Oscillation theory of functional-differential equations (34K11) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for functional-differential equations (65L03)

Related Items (6)

Stability ofθ-schemes for partial differential equations with piecewise constant arguments of alternately retarded and advanced type ⋮ Preservation of stability and oscillation of Euler-Maclaurin method for differential equation with piecewise constant arguments of alternately advanced and retarded type ⋮ Convergence and stability of the one-leg θ method for stochastic differential equations with piecewise continuous arguments ⋮ Stability and oscillation of mixed differential equation with piecewise continuous arguments ⋮ Stability of numerical solution for partial differential equations with piecewise constant arguments ⋮ Numerical oscillation and non-oscillation for differential equation with piecewise continuous arguments of mixed type

Cites Work

• Oscillation analysis of numerical solution in the \(\theta\)-methods for equation \(x\prime (t) + ax(t) + a_{1}x([t - 1) = 0\)]
• 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
• Order stars and stability theorems

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