Reliable Approximate Solution of Systems of Volterra Integro-Differential Equations with Time-Dependent Delays

Authors:
M. Shakourifar;W. H. Enright
Affiliations:
shakouri@cs.toronto.edu and enright@cs.toronto.edu;-
Venue:
SIAM Journal on Scientific Computing
Year:
2011

Citing 10
Cited 0

Analysis of error control strategies for continuous Runge-Kutta methods

SIAM Journal on Numerical Analysis
Some applications of continuous Runge-Kutta methods

Applied Numerical Mathematics - Special issue celebrating the centenary of Runge-Kutta methods
Continuous Runge-Kutta methods for neutral Volterra integro-differential equations with delay

Selected papers of the second international conference on Numerical solution of Volterra and delay equations : Volterra centennial: Volterra centennial
Numerical modelling in biosciences using delay differential equations

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Numerical stability of nonlinear delay differential equations of neutral type

Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Solving ODEs and DDEs with residual control

Applied Numerical Mathematics
Robust and reliable defect control for Runge-Kutta methods

ACM Transactions on Mathematical Software (TOMS)
On the numerical solution of nonlinear systems of Volterra integro-differential equations with delay arguments

Computing
Recent advances in the numerical analysis of Volterra functional differential equations with variable delays

Journal of Computational and Applied Mathematics
Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview

Applied Numerical Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Volterra integro-differential equations with time-dependent delay arguments can provide us with realistic models of many real-world phenomena. Delayed Lokta-Volterra predator-prey systems arise in Ecology and are well-known examples of delay Volterra integro-differential equations (DVIDEs) first introduced by Volterra in 1928. We investigate the numerical solution of systems of DVIDEs using an adaptive stepsize selection strategy. We will present a generic variable stepsize approach for solving systems of neutral DVIDEs based on an explicit continuous Runge-Kutta method using defect error control and study the convergence of the resulting numerical method for various kinds of delay arguments. We will show that the global error of the numerical solution can be effectively and reliably controlled by monitoring the size of the defect of the approximate solution and adjusting the stepsize on each step of the integration. Numerical results will be presented to demonstrate the effectiveness of this approach.