求解拉普拉斯方程柯西问题的截断赫尔米特展开方法

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 457-468.

求解拉普拉斯方程柯西问题的截断赫尔米特展开方法

谢瓯¹, 孟泽红², 赵振宇¹, 由雷¹

1. 广东海洋大学数学与计算机学院广东湛江 524008;
2. 浙江财经大学数学与统计学院杭州 310018

收稿日期:2016-09-27 修回日期:2017-01-21 出版日期:2017-06-26 发布日期:2017-06-26
作者简介:谢瓯,E-mail:wozitianshanglai@163.com;孟泽红,E-mail:dongdongzb@gmail.com
基金资助:
国家自然科学基金（11201085）和广东海洋大学创新强校工程项目（2014050216）

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

Xie Ou¹, Meng Zehong², Zhao Zhenyu¹, You Lei¹

1. Faculty of Mathematics and Computer Science, Guangdong Ocean University, Guangdong Zhanjiang 524088;
2 School of Mathematics and Statistics, Zhejiang University of Finance & Economics, Hangzhou 310018

Received:2016-09-27 Revised:2017-01-21 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the NSFC (11201085) and the Guandong Ocean University Innovation Strong School Projects (2014050216)

摘要/Abstract

摘要： 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.

关键词: 不适定问题, 拉普拉斯方程柯西问题, 偏差原理, 截断方法

Abstract: 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.

Key words: Ill-posed problem, Cauchy problem for Laplace equation, Regularization, Discrepancy principle, Truncation method

中图分类号:

O124

谢瓯, 孟泽红, 赵振宇, 由雷. 求解拉普拉斯方程柯西问题的截断赫尔米特展开方法[J]. 数学物理学报, 2017, 37(3): 457-468.

Xie Ou, Meng Zehong, Zhao Zhenyu, You Lei. A Truncation Method Based on Hermite Functions Expansion for a Cauchy Problem of the Laplace Equation[J]. Acta mathematica scientia,Series A, 2017, 37(3): 457-468.

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