On the construction of solutions of general linear boundary value problems for systems of functional differential equations

Abstract

R n , we describe a method of construction of its solution using successive approximations by the sequence of the solutions of simple boundary value problems. We prove the conditions which guarantee the convergence of the above mentioned sequences in general and special cases, we prove the stability of the convergence in some sense. Also, for illustration, we solve some typical problems in MAPLE.

On Construction of Solutions of Linear Differential Systems with Argument Deviations of Mixed Type

“…In certain cases, boundary conditions are more complicated and deviations are of mixed type (i. e., equations involve both retarded and advanced terms [7,8] or deviations of neither type), which in particular, makes impossible to apply the method of steps due to the absence of the Volterra property of the corresponding operator. The aim of this paper is to show that the techniques suggested in [9] for boundary value problems for ordinary differential equations, under certain assumptions, can be adopted for application to functional differential equations covering, in particular, the case of deviations of mixed type and general boundary conditions.…”