三维Laplace方程柯西问题具有Dirichlet核的软化正则解  

A Mollification Method with Dirichlet Kernel to Solve the Cauchy Problem for the Three-dimensional Laplace Equation

作　　者：何尚琴 冯秀芳 HE Shangqin;FENG Xiufang(School of Mathematics and Information Science,North Minzu University,Yinchuan 750021,Ningxia;School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,Ningxia)

机构地区：[1]北方民族大学数学与信息科学学院,宁夏银川750021 [2]宁夏大学数学统计学院,宁夏银川750021

出　　处：《四川师范大学学报（自然科学版）》2021年第1期55-62,共8页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11961054);宁夏自然科学基金(NZ16011和2020AAC03253)。

摘　　要：研究一类三维Laplace方程Cauchy问题,该问题是严重不适定的.为了获得其稳定的数值解,利用二维Dirichlet核构造软化算子,得到正则逼近解的显式形式,在先验参数的选取规则之下,给出正则近似解与精确解之间的误差估计,并通过数值实验检验方法的有效性和稳定性.The Cauchy problem for the Laplace equation is a severely ill-posed problem.In this paper,to obtain the stable numerical solution for this problem,a mollification method with the two-dimensional Dirichlet kernel is proposed to construct regularization approximation solution,and the error estimate between the regularization approximation solution and the exact solution is given.Finally,a numerical example is presented to show the effectiveness of the proposed method.

关 键 词：三维Laplace方程 不适定 二元Dirichlet核 软化法 误差估计 数值实验 

分 类 号：O241.8[理学—计算数学]