Numerical Algorithm for Simultaneously Determining of Unknown Coefficients in a Parabolic Equation

摘要

A numerical algorithm for an inverse problem of simultaneously determining unknown coefficients in a linear parabolic equation subject to the specifications of the solution at internal points along with the usual initial and boundary conditions is proposed. The approach based on TTF (Trace Type Functional) formulation of the problem is used. To avoid instability in this approach the Tikhonov regularization method is applied. Some numerical examples using the proposed algorithm are presented.