An iteration method for initial-value problems of retarded differential equations. (English) Zbl 0538.65046

Strehmel, Karl; Chocholatý, Pavol

Acta Math. Univ. Comenianae 42-43, 249-254 (1983).

This paper deals with an iterative method for solving the retarded differential equation \(x'(t)=f(t,x(t),\quad x(\alpha(t))),\) 0\(\leq t\leq T\), \(\alpha\) (t)\(\leq t\), \(x(t)=\phi(t)\), \(T\leq t\leq 0\). In this method the above problem is reduced to a sequence of initial-value problems for a system of ordinary differential equations. These systems can be solved using numerical methods for ordinary differential equations.

Reviewer: R.S.Dahiya

MSC:

65L05	Numerical methods for initial value problems
34K05	General theory of functional-differential equations

Keywords:

iteration method; retarded differential equations