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Tikhonov type regularization method for the Cauchy problem of the modified Helmholtz equation

Authors
Journal
Applied Mathematics and Computation
0096-3003
Publisher
Elsevier
Publication Date
Volume
203
Issue
2
Identifiers
DOI: 10.1016/j.amc.2008.05.007
Keywords
  • Cauchy Problem
  • Modified Helmholtz Equation
  • Tikhonov Type Regularization
  • Convergence Analysis
  • Error Estimation
Disciplines
  • Computer Science

Abstract

Abstract In this paper, we propose a numerical method for solving the Cauchy problem of the modified Helmholtz equation. By using Green’s formula, the Cauchy problem is transformed to a moment problem. Then we propose a Tikhonov type regularization algorithm for obtaining an approximate solution to the Neumann date on the unspecified boundary. Convergence analysis and error estimation are also discussed. For numerical verification, several numerical examples in the two-dimensional case are presented.

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