Numerical methods for delay models in biomathematics

DOI10.1007/88-470-0396-2_5zbMath1387.92007OpenAlexW4631914MaRDI QIDQ4638232

Stefano Maset, Nicola Guglielmi, Alfredo Bellen

Publication date: 4 May 2018

Published in: Complex Systems in Biomedicine (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/88-470-0396-2_5

zbMATH Keywords

delay differential equationsstate dependent delaycontinuous Runge-Kutta methodsRadau IIA methodsfunctional Runge-Kutta methodsWaltman model

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) General biology and biomathematics (92B05)

Related Items (6)

Splitting extrapolation algorithms for solving linear delay Volterra integral equations with a spatial variable ⋮ Periodic, Quasi-Periodic and Phase-Locked Oscillations and Stability in the Fiscal Dynamical Model with Tax Collection and Decision-Making Delays ⋮ Stage-based interpolation Runge-Kutta methods for nonlinear Volterra functional differential equations ⋮ Normal and pathological dynamics of platelets in humans ⋮ Complicated oscillations and non-resonant double Hopf bifurcation of multiple feedback delayed control system of the gut microbiota ⋮ High-order collocation methods for nonlinear delay integral equation

Uses Software

• RADAU
• RODAS
• RADAR5

Cites Work

• Delay differential equations: with applications in population dynamics
• Differential-difference equations
• Computing breaking points in implicit delay differential equations
• Numerical treatment of retarded differential-algebraic equations by collocation methods
• A delay differential equation solver based on a continuous Runge-Kutta method with defect control
• On the Newton iteration in the application of collocation methods to implicit delay equations
• Theory and applications of partial functional differential equations
• Introduction to the theory and application of differential equations with deviating arguments. Translated from the Russian by John L. Casti
• Delay equations. Functional-, complex-, and nonlinear analysis
• Issues in the numerical solution of evolutionary delay differential equations
• Stiff differential equations solved by Radau methods
• A problem in the theory of epidemics
• Predator-prey equations simulating an immune response
• High Order Methods for State-Dependent Delay Differential Equations with Nonsmooth Solutions
• Existence and uniqueness of solutions of a functional differential equation modeling thresholds
• Numerical Methods for Delay Differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations
• The Numerical Solution of Volterra Functional Differential Equations by Euler’s Method
• RUNGE–KUTTA METHODS FOR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS
• Implementing Radau IIA methods for stiff delay differential equations
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