西北师范大学学报（自然科学版）2017，Vol.53Issue(3)：1-7,7.DOI:10.16783/j.cnki.nwnuz.2017.03.001
修改的Helmholtz方程Cauchy问题的一种软化方法
A mollification method for solving the Cauchyproblem for the modified Helmholtz equation
摘要
Abstract
The Cauchy problem for the modified Helmholtz equation is a severely ill-posed problem.In this paper,to obtain the stable numerical solution for this problem,a mollification method(using the Gaussian kernel) is proposed to construct regularization approximation solution,and then the error estimate between regularization approximation solution and exact solution is given.Finally,a numerical example is given to show the effectiveness of the proposed method.关键词
不适定问题/反问题/修改的Helmholtz方程/正则化/误差估计Key words
ill-posed problem/inverse problem/modified Helmholtz equation/regularization/error estimate分类
数理科学引用本文复制引用
熊向团,毛东玲,曹笑笑..修改的Helmholtz方程Cauchy问题的一种软化方法[J].西北师范大学学报（自然科学版）,2017,53(3):1-7,7.基金项目
国家自然科学基金资助项目(11661072) （11661072）
