Asymptotic stability of Runge-Kutta methods for nonlinear differential equations with piecewise continuous arguments

DOI10.1016/j.cam.2014.11.059zbMath1309.65084OpenAlexW1967035519MaRDI QIDQ484875

Ming-Zhu Liu, Xing Liu

Publication date: 8 January 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2014.11.059

zbMATH Keywords

asymptotic stabilitydelay differential equationsRunge-Kutta methodsnumerical solutionspiecewise continuous arguments

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (5)

Stability analysis of parabolic partial differential equations with piecewise continuous arguments ⋮ Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument ⋮ Convergence and stability of the split-step theta method for stochastic differential equations with piecewise continuous arguments ⋮ Block boundary value methods applied to functional differential equations with piecewise continuous arguments ⋮ Stability analysis of analytical and numerical solutions to nonlinear delay differential equations with variable impulses

Uses Software

• RODAS

Cites Work

• The improved linear multistep methods for differential equations with piecewise continuous arguments
• Retarded differential equations with piecewise constant delays
• Advanced differential equations with piecewise constant argument deviations
• Stability of the Euler-Maclaurin methods for neutral differential equations with piecewise continuous arguments
• Stability analysis of Runge-Kutta methods for unbounded retarded differential equations with piecewise continuous arguments
• Dissipativity of Runge-Kutta methods for neutral delay differential equations with piecewise constant delay
• On the solvability of the systems of equations arising in implicit Runge- Kutta methods
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• Contractivity of continuous Runge-Kutta methods for delay differential equations
• Stability of Runge--Kutta methods in the numerical solution of equation \(u'(t)=au(t)+a_{0}u([t)\).]
• Stability of solutions of nonlinear neutral differential equations with piecewise constant delay and their discretizations
• Stability of \(\theta\)-methods for advanced differential equations with piecewise continuous arguments
• Stability of Runge-Kutta methods for the alternately advanced and retarded differential equations with piecewise continuous arguments
• High Order Contractive Runge–Kutta Methods for Volterra Functional Differential Equations
• Tricks or Treats with the Hilbert Matrix
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