热传导方程反问题的Tikhonov正则化法

Tikhonov Regularization Method on Inverse Problem of Heat Conduction Equation

为了分析热传导方程反问题所涉及的初始条件。论文把这一类问题转化成第一类Fredholm积分方程,运用Tikhonov正则化的反演法和牛顿法获取正则化参数,得到这一问题的数值解。通过数值实验,验证了这一算法在实际应用中的有效性。

In order to analyze initial conditions of inverse problem of heat conduction equation, it is transformed into a Fredholm＇s integral equation of the first kind, numerical solution of this problem is obtained by using Tikhonov regularization inversion method and Newton＇s method to obtain the regularization parameter, Through the experiment, the validity of this algorithm is verified in practical application.