Existence and approximation of a solution of boundary value problems for delay integro-differential equations

Abstract

The properties of a solution of the boundary value problems for delay integro-differential equations are investigated, the conditions for the existence and uniqueness of their solution are found. An iterative scheme of finding an approximate solution using cubic splines with defect two is suggested. The sufficient conditions for the convergence of the iterative scheme are obtained.

Keywords

• boundary value problems
• spline functions
• delay integro-differential equations
• cubic splines