A method of solving boundary value problems

Abstract IN this paper search algorithms (optimal with respect to two different criteria) are found for the extrema of unimodal functions of one variable which satisfy a Lipschitz condition. The algorithms obtained are a generalization of the well-known Kiefer-Johnson method [1, 2]. In Section 1 the method is demonstrated by an example of two differential equations, in Section 2 it is considered for an n -dimentional set of equations and in Section 3 its application to linear boundary value problems is investigated in details.