逆热传导方程的一类正则化算法

A Regularization Algorithm for Solving the Sideways Heat Equation

考虑了标准的一维逆热传导方程,问题是不适定的,即解不连续地依赖于数据。通过Fourier逼近的方法进行正则化处理,提出了一类新的算法并且与已有的正则化算法进行了比较,理论分析和数值实验均表明该算法是稳定的,且具有相同的精度和计算复杂性,同时也具有灵活性和广泛性。

The standard sideways inverse heat conduction equation is discussed. The problem is ill-posed, in the sense that the solution （if it exists） does not depend continuously on the data. It is regularized by a Fourier-based approximation. A new algorithm is proposed and compared with the current regularization algorithm. Theoretical analyses and numerical experiments show that it is stable, flexible and universal with the same degree of accuracy and computational complexity.