##
**Numerical solution of two-point boundary value problems for retarded differential equations.**
*(English)*
Zbl 0731.65067

This paper is concerned with the numerical solution of two-point boundary value problems for certain types of delay differential equations. The problems under consideration have the form: \(y'(t)=f(t,y(\alpha (t)),\) \(t\in [a,b],\) \(B_ 1y(a)+B_ 2y(b)=\beta,\) with \(\alpha (a)=a\) and \(a\leq \alpha (t)\leq t\). To solve these problems the well known idea of the shooting method is applied. The author follows closely the treatment given by H. B. Keller [SIAM J. Numer. Anal. 11, 305-320 (1974; Zbl 0282.65065)] and J. Stoer and R. Bulirsch [Introduction to numerical analysis (1980; Zbl 0423.65002); for the German original editions see Zbl 0245.65001 and Zbl 0257.65001] for two-point boundary value problems for ordinary differential equations.

Then, assuming that the original problem has a unique solution, together with some further assumptions, it is finally proved that the shooting method applied to the problem has a unique solution.

Then, assuming that the original problem has a unique solution, together with some further assumptions, it is finally proved that the shooting method applied to the problem has a unique solution.

Reviewer: M.Calvo (Zaragoza)

### MSC:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34K10 | Boundary value problems for functional-differential equations |