The Method of the Integral Equations to Construct the Green's Function

Linear differential operator and the system of the boundary conditions were considered. The boundary conditions are linear and linear independent functionals. The Green's function for the defined by this operator and functionals boundary problem was build as solution of the Fredholm's integral equation of the second kind. Characteristics of the Fredholm's equation was defined by the Green's function of the auxiliary problem. Resulting Green's function makes it possible to solve both direct (the problem of finding solutions) and inverse (the problem of finding the right part of the equation from the experimentally obtained solution) problems. The numerical algorithm to solve boundary problem and inverse problem was build on the basis of the proposed method and tested.