热传导方程反问题未知边界的稳定数值算法

A Stable Numerical Algorithm for a Heat Conduction Inverse Problem with Unknown Right Boundary

热传导方程反问题在物理学中模拟均匀的多孔介质流时经常会被碰到,该类问题由一个右边界未知的线性热传导方程以及在指定内点上测量所得的数据条件构成.为了能够求解该类线性反问题,将首先证明解的唯一性,然后给出全新的离散后有限差分格式求解该反问题.讨论了该格式的稳定性,最后给出数值试验,以此来表明该方法的有效性和可行性.

A one -dimensional heat conduction inverse problem is a common one in the study of the simulation of homogeneous porous medium flow in physics. This problem consists of a linear heat conduction equation unknown at the right boundary and a data condition measured at an interior specified point. In order to solve this linear inverse problem, the uniqueness of the solution is firstly proven. Then, a new finite difference scheme after a complete discretization is given for the solution to the inverse problem. Stability conditions for numerical solution to the inverse problem are also discussed. Finally, numerical results of experiments are provided to prove the feasibility and effectiveness of the methods suggested.