Petr Tomášek

Visualization and Analysis of Stability Regions of Certain Discretization of Differential Equation with Constant Delay

abstract:
The paper discusses the asymptotic stability regions of multistep discretization of linear delay differential equation with a constant delay. Different location of delay dependent parts of stability regions with respect to parity of number of steps clarifies unexpected changes in numerical solution's behaviour under various settings of the equation's parameters and stepsize.

Mathematics Subject Classification: 34K28, 34K20

Key words and phrases: Delay differential equation, constant delay, difference equation, numerical solution, necessary and sufficient conditions for asymptotic stability