Symbolic Algorithm for Solving Nonlocal Boundary Value Problems for Systems of Ordinary Integrodifferential Equations

Boundary value problems for systems of integrodifferential equations appear in many branches of science and engineering. Accuracy in modeling complex processes requires the specification of nonlocal boundary conditions, including multipoint and integral conditions. These kinds of problems are even harder to solve. In this paper, we present solvability criteria and a direct operator method for constructing the exact solution to systems of linear ordinary integrodifferential equations with general nonlocal boundary conditions. A symbolic algorithm is also proposed. Several examples are solved to demonstrate the effectiveness of the method. The results obtained are equally valid for nonlocal boundary value problems for systems of ordinary differential, loaded differential, and loaded integrodifferential equations.