On the discretization of differential and Volterra integral equations with variable delay
This paper deals with discretization techniques applied to differential and Volterra integral equations of the second kind with variable delay. Collocation and iterated collocation methods are used for solving these equations and the problem of the attainable order of \(m\)-stage implicit Runge-Kutta methods with variable delays (of the form \(qt\), \(0< q< 1)\) is studied. It is proved that, in contrast to equations without delay, or equations with constant delay, collocation at the Gauss (-Legendre) points will no longer yield the optimal (local) order \(O(h^{2m})\). A numerical linear example is given.
scientific article; zbMATH DE number 1000359
scientific article