The asymptotic behaviour of theθ-methods with constant stepsize for the generalized pantograph equation

DOI10.1080/00207160.2015.1061124zbMath1365.65181OpenAlexW2301654937MaRDI QIDQ2957737

Gengen Zhang, Ai-Guo Xiao, Wan-Sheng Wang

Publication date: 27 January 2017

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2015.1061124

zbMATH Keywords

numerical examplesasymptotic stabilityasymptotic behaviour\(\theta\)-methodsneutral functional differential equationsgeneralized pantograph equation

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Neutral functional-differential equations (34K40) Numerical methods for functional-differential equations (65L03)

Related Items

An alternative use of fuzzy transform with application to a class of delay differential equations ⋮ A new numerical method to solve pantograph delay differential equations with convergence analysis ⋮ Modified Chebyshev collocation method for pantograph-type differential equations

Cites Work

• On neutral functional-differential equations with proportional delays
• A family of solutions of the IVP for the equation \(x'(t)=ax(\lambda t), \lambda>1\)
• Stability of continuous Runge-Kutta-type methods for nonlinear neutral delay-differential equations
• Nonlinear stability of general linear methods for neutral delay differential equations
• On the contractivity and asymptotic stability of systems of delay differential equations of neutral type
• Exact and discretized stability of the pantograph equation
• Numerical stability of nonlinear delay differential equations of neutral type
• Nonlinear stability of one-leg methods for delay differential equations of neutral type
• Nonlinear stability of Runge-Kutta methods for neutral delay differential equations
• On the asymptotics of the trapezoidal rule for the pantograph equation
• The stability and asymptotic properties of the  -methods for the pantograph equation
• Stability analysis of general linear methods for the nonautonomous pantograph equation
• On neutral functional-differential equations with variable time delays
• The functional-differential equation y′(t)=Ay(t) +By(qt) +Cy′(qt) +f(t)
• Stability of one-leg  -methods for the variable coefficient pantograph equation on the quasi-geometric mesh
• Numerical Methods for Delay Differential Equations
• Stability and Asymptotic Stability of Functional-Differential Equations
• Asymptotic behaviour of functional-differential equations with proportional time delays
• The functional-differential equation $y'\left( x \right) = ay\left( {\lambda x} \right) + by\left( x \right)$
• Discretized Stability and Error Growth of The Nonautonomous Pantograph Equation