Inverse Problem for Reconstructing the Right Side of a One-Dimensional Wave Equation

Abstract

An inverse problem of recovering the unknown parameter of an external source for a one-dimensional wave equation with a nonlocal additional condition is considered. It is assumed that the unknown source parameter depends only on time. By integration, the problem is transformed to an inverse boundary value problem with local conditions. A difference analogue of the differential problem in the form of an implicit difference scheme is constructed and a non-iterative computational algorithm for solving the resulting system of difference equations is proposed. As a result, an explicit formula is obtained for determining the approximate value of the sought parameter for each discrete value of the time variable