We consider a variable-structure optimal control problem described in different domains by hyperbolic integro-differential equation and Volterra integral equation, respectively. The quality functional is terminal. A formula for the increment of criterion constructed an analogue L.S. Pontryagin's maximum principle proved investigating on special McShane-type variations.

In this paper, the Dirac type integro differential system\ with a nonlocal integral boundary condition is considered. First, we derive asymptotic expressions for solutions and large eigenvalues. Second, provide nodal points prove that dense subset of uniquely determines parameter potential function considered system. We also an effective procedure solving inverse problem.

The spline collocation method  is employed to solve a system of linear and nonlinear Fredholm and Volterra integro-differential equations. The solutions are collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula. We obtain the unique solution for linear and nonlinear system $(nN+3n)times(nN+3n)$ of integro-differential equations. This approximation reduces th...