Analytical and numerical dissipativity for nonlinear generalized pantograph equations

DOI10.3934/DCDS.2011.29.1245zbMath1225.65068OpenAlexW2328731908MaRDI QIDQ632365

Cheng-Jian Zhang, Wan-Sheng Wang

Publication date: 15 March 2011

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2011.29.1245

zbMATH Keywords

numerical experimentsdissipativityinfinite delaybackward Euler methodneutral delay differential equationsgeneralized pantograph equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Neutral functional-differential equations (34K40) Numerical methods for functional-differential equations (65L03)

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Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations ⋮ Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson's blowflies models ⋮ Analytical and numerical dissipativity for the space-fractional Allen-Cahn equation ⋮ Long time behavior of non-Fickian delay reaction-diffusion equations ⋮ Stability of exact and discrete energy for non-Fickian reaction-diffusion equations with a variable delay ⋮ Dissipativity of Runge-Kutta methods for a class of nonlinear functional-integro-differential equations ⋮ Generalized polynomial chaos for nonlinear random pantograph equations ⋮ Long time numerical behaviors of fractional pantograph equations ⋮ Long time \(\mathcal{H}_\alpha^s\) stability of a classical scheme for Cahn-Hilliard equation with polynomial nonlinearity

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