The Inverse Problem of the Simultaneous Determination of the Right-Hand Side and the Lowest Coefficients in Parabolic Equations

Abstract

In this paper, we propose a numerical scheme to solve the inverse problem of determining two lower coefficients that depends on time only in the parabolic equation. The time dependence of the right-hand side of a parabolic equation is determined using additional solution values at points of the computational domain. For solving the nonlinear inverse problem, linearized approximations in time are constructed using the fully implicit scheme, and standard finite difference procedures are used in space. The results of numerical experiments are presented, confirming the capabilities of the proposed computational algorithms for solving the coefficients inverse problem.