Simultaneous determination of unknown coefficients in a parabolic equation

Abstract

A numerical method for an inverse problem of simultaneously determining unknown coefficients in a parabolic equation subject to the specifications of the solution at boundary points and given integral of the solution on space variable along with the usual initial and boundary conditions is proposed. The approach based on 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.

Keywords:

• parabolic equation
• inverse problem
• unknown coefficients
• finite-difference method
• numerical algorithm
• Tikhonov regularization

Acknowledgement

This research was supported by The Scientific and Technical Research Council of Turkey, TUBITAK, project number 104T137.