A Regularization Method to Solve a Cauchy Problem for the Two-Dimensional Modified Helmholtz Equation

被引：4

作者：

He, Shangqin ^{[1
,2
]}

Feng, Xiufang ^{[1
]}

机构：

[1] NingXia Univ, Sch Math & Stat, Yinchuan 750021, Peoples R China

[2] Hebei Normal Univ Sci & Technol, Coll Math & Informat Sci & Technol, Qinhuangdao 066004, Hebei, Peoples R China

来源：

MATHEMATICS | 2019年 / 7卷 / 04期

基金：

美国国家科学基金会;

关键词：

modified Helmholtz equation; ill-posed; de la Vallee Poussin kernel; mollification method; regularization solution; error estimate; 26D15; 31A25; 31B20; 31B35; MOLLIFICATION METHOD; ELEMENT SOLUTION;

D O I：

10.3390/math7040360

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the ill-posed problem of the two-dimensional modified Helmholtz equation is investigated in a strip domain. For obtaining a stable numerical approximation solution, a mollification regularization method with the de la Vallee Poussin kernel is proposed. An error estimate between the exact solution and approximation solution is given under suitable choices of the regularization parameter. Two numerical experiments show that our procedure is effective and stable with respect to perturbations in the data.

引用

页数：13

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