求解拉普拉斯方程柯西问题的截断赫尔米特展开方法

A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation

该文研究一类拉普拉斯方程的柯西问题.为了获得稳定的数值解,采用了基于赫尔米特函数展开的截断方法来克服问题的不适定性.通过偏差原理选取截断参数并建立了相应的误差估计.数值结果同样显示方法是有效的.

We investigate a Cauchy problem for the Laplace equation in this paper. To obtain a stable numerical solution for this ill posed problem, we present a truncation method based on Hermite functions expansion. Error estimate are obtained together with a discrepancy principle for the regularization parameter. Some numerical tests show that the method works effectively.