Error Estimate of Numerical Method for Solving an Inverse Problem

Abstract

Linear differential operator and the system of boundary conditions were considered. The
boundary conditions are linear and linear independent functionals. The Green functions for
the boundary problem defined by this operator and the functionals was build as a solution
of the Fredholm integral equation of the second kind. Characteristics of the Fredholm
equation was defined by the Green function of the auxiliary problem. The suggested method
enables 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 characteristics of the numerical implementation of the method and the possibility of
assessing the accuracy of the solutions were discussed.