Dynamics of constant and variable stepsize methods for a nonlinear population model with delay

DOI10.1016/S0168-9274(97)00037-8zbMath0899.92027MaRDI QIDQ1360562

Tasneem K. Sardar, Desmond J. Higham

Publication date: 10 November 1998

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

zbMATH Keywords

delayperiodic boundary conditionsinitial conditionsHutchinson's equationEuler's methodadaptive time-stepping approach

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Related Items (7)

The compact and Crank-Nicolson ADI schemes for two-dimensional semilinear multidelay parabolic equations ⋮ On convergence of difference schemes for delay parabolic equations ⋮ Almost periodic solutions of partial differential equations with delay ⋮ The study of a fourth-order multistep ADI method applied to nonlinear delay reaction-diffusion equations ⋮ Well-posedness of delay parabolic difference equations ⋮ D-convergence and conditional GDN-stability of exponential Runge-Kutta methods for semilinear delay differential equations ⋮ Computational methods for delay parabolic and time-fractional partial differential equations

Cites Work

• Regularity properties of Runge-Kutta methods for delay differential equations
• Equilibrium states of adaptive algorithms for delay differential equations
• Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay
• Nonnormality effects in a discretised nonlinear reaction-convection-diffusion equation
• Equilibrium states of Runge Kutta schemes
• Stable Periodic Bifurcations of an Explicit Discretization of a Nonlinear Partial Differential Equation in Reaction Diffusion
• On spurious asymptotic numerical solutions of explicit Runge-Kutta methods
• Spurious solutions of numerical methods for initial value problems
• Stability and Dynamics of Numerical Methods for Nonlinear Ordinary Differential Equations
• Does Error Control Suppress Spuriosity?
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