A numerical method for solving a nonlinear inverse parabolic problem

Abstract

This study is motivated by a desire to obtain a numerical approach combining the use of the finite difference method with the solution of ordinary differential equation proposed for the determination of unknown coefficient in an inverse heat conduction problem. To regularize the resultant ill-conditioned linear system of equations, we apply the Tikhonov regularization method to obtain the stable numerical approximation to the solution.

Keywords:

• inverse heat conduction problem
• stability
• finite difference method
• least-squares method
• regularization method

AMS Subject Classifications::

• 58J35
• 65N21
• 65Y99