A mollification method with Dirichlet kernel to solve Cauchy problem for two-dimensional Helmholtz equation-Reference-Cited by-同舟云学术

A mollification method with Dirichlet kernel to solve Cauchy problem for two-dimensional Helmholtz equation

Published:2019-09 Issue:05 Volume:17 Page:1950029
ISSN:0219-6913
Container-title:International Journal of Wavelets, Multiresolution and Information Processing
language:en
Short-container-title:Int. J. Wavelets Multiresolut Inf. Process.

Author:

He Shangqin¹²,Feng Xiufang²

Affiliation:

1. School of Mathematics and Statistics, NingXia University, Yinchuan 750021, P. R. China

2. College of Mathematics and Information Science and Technology, Hebei Normal University of Science and Technology, Qinhuangdao 066004, P. R. China

Abstract

In this paper, the ill-posed Cauchy problem for the Helmholtz equation is investigated in a strip domain. To obtain stable numerical solution, a mollification regularization method with Dirichlet kernel is proposed. Error estimate between the exact solution and its approximation is given. A numerical experiment of interest shows that our procedure is effective and stable with respect to perturbations of noise in the data.

Funder

National Natural Science Foundation of China

Natural Science Foundation of Ningxia Province

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Information Systems,Signal Processing

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219691319500292

Reference21 articles.

1. Stable Solution of Inverse Problems

2. The Fourier regularization for solving the Cauchy problem for the Helmholtz equation

3. A mollification method for ill-posed problems

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