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A nonlinear system of differential equations with distributed delays

Chocholatý, Pavol — 2010

Programs and Algorithms of Numerical Mathematics

It is well-known that the environments of most natural populations change with time and that such changes induce variation in the growth characteristics of population which is often modelled by delay differential equations, usually with time-varying delay. The purpose of this article is to derive a numerical solution of the delay differential system with continuously distributed delays based on a composition of p -step methods ( p = 1 , 2 , 3 , 4 , 5 ) and quadrature formulas. Some numerical results are presented compared...

Integro-differential equations with time-varying delay

Chocholatý, Pavol — 2013

Programs and Algorithms of Numerical Mathematics

Integro-differential equations with time-varying delay can provide us with realistic models of many real world phenomena. Delayed Lotka-Volterra predator-prey systems arise in ecology. We investigate the numerical solution of a system of two integro-differential equations with time-varying delay and the given initial function. We will present an approach based on q -step methods using quadrature formulas.

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