求解椭圆方程柯西问题的修正吉洪诺夫正则化方法

Solving Cauchy problem of elliptic equation by modified Tikhonov regularization method

研究了一类变系数椭圆方程的柯西问题,这类问题出现在很多实际问题领域.由于问题的不适定性,不可能通过经典的数值方法来求解上述问题,必须引入正则化手段.采用了一种修正吉洪诺夫正则化方法来求解上述问题.在一种先验和一种后验参数选取准则下,分别获得了问题的误差估计.数值例子进一步显示方法是稳定有效的.

A Cauchy problem of an elliptic equation with variable coefficients is considered. This problem occurs in the study of many practical problems, and it is ill posed. Therefore, it is impossible to solve the problem using classical numerical methods and special techniques are required. A modified Tikhonov regularization method is presented, and the error estimates are obtained with a priori strategy and a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable.