A Numerical Approximation to the Solution of an Inverse Heat Conduction Problem

作者：Azari Hossein; Zhang Shuhua^*

来源：Numerical Methods for Partial Differential Equations, 2010, 26(1): 95-106.

DOI：10.1002/num.20418

• inverse problem
• numerical method
• uniqueness

The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing new variable, we reformulate the problem as a nonclassical parabolic equation along with the initial and boundary conditions. The uniqueness and continuous dependence of the solution upon the data are demonstrated, and then finite difference methods, backward Euler and Crank-Nicolson schemes are studied. The results of some numerical examples are presented to demonstrate the efficiency and the rapid convergence of the methods.

• 出版日期2010-1
• 单位天津财经大学