Homogenized functions to recover H(t)/H(x) by solving a small scale linear system of differencing equations

作者：Liu, Chein-Shan^*

来源：International Journal of Heat and Mass Transfer, 2016, 101: 1103-1110.

DOI：10.1016/j.ijheatmasstransfer.2016.05.133

• Heat source recovery problem
• Pascal polynomials
• Eigenfunctions
• Homogenized functions
• Differencing equations

In order to recover the unknown heat source H(t)/H(x) in the heat conduction equation, we introduce homogenized functions and differencing equations, which can significantly simplify the solution procedures for the inverse heat source recovery problem. We only need to solve a few linear equations in the problem domain, since the initial condition boundary conditions and a supplementary condition are satisfied automatically, and the differencing technique is employed to eliminate the heat source terms in the linear equations. The Pascal polynomials and eigenfunctions are adopted as trial functions to expand the trial solutions, and then some small scale linear systems are solved to determine the expansion coefficients. Because the ill-posedness of the inverse heat source recovery problem is greatly reduced, the present methods are accurate and stable against large noise up to 20%, which are confirmed by the numerical tests.

• 出版日期2016-10
• 单位河海大学