Journal ArticleDOI
Quasi-reversibility and truncation methods to solve a Cauchy problem for the modified Helmholtz equation
Hai-Hua Qin,Ting Wei +1 more
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TLDR
A quasi-reversibility method and a truncation method are used to solve the Cauchy problem for the modified Helmholtz equation in a rectangular domain and convergence estimates under two different a priori boundedness assumptions for the exact solution are presented.About:
This article is published in Mathematics and Computers in Simulation.The article was published on 2009-10-01. It has received 42 citations till now. The article focuses on the topics: Cauchy problem & Truncation error (numerical integration).read more
Citations
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Journal ArticleDOI
An alternating iterative MFS algorithm for the Cauchy problem for the modified Helmholtz equation
TL;DR: In this article, the authors investigated the numerical implementation of the alternating iterative algorithm originally proposed by Kozlov et al. for the Cauchy problem associated with the two-dimensional modified Helmholtz equation using a meshless method.
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Some remarks on a modified Helmholtz equation with inhomogeneous source
TL;DR: In this paper, Qin et al. introduced new efficient regularization methods, such as truncation of high frequency and quasi-boundary-type methods, with explicit error estimates for an extended case (i.e. the inhomogeneous problem with f ≠ 0 in Eq. (1) ).
Journal ArticleDOI
A meshless method for solving the nonlinear inverse Cauchy problem of elliptic type equation in a doubly-connected domain
TL;DR: The accuracy and robustness of the homogenization boundary function method (HBFM) are examined through seven numerical examples, where the exact Dirichlet data on the inner boundary are compared to the ones recovered by the HBFM under a large noisy disturbance.
Journal ArticleDOI
Landweber iterative regularization method for identifying the unknown source of the modified Helmholtz equation
Fan Yang,Xiao Liu,Xiao-Xiao Li +2 more
TL;DR: In this paper, the authors consider the inverse problem of identifying the unknown source for the modified Helmholtz equation and propose the Landweber iterative regularization method to solve this problem and obtain the regularization solution.
Journal ArticleDOI
A novel mixed group preserving scheme for the inverse Cauchy problem of elliptic equations in annular domains
Chein-Shan Liu,Chih-Wen Chang +1 more
TL;DR: In this article, a combination of the spring-damping regularization method (SDRM) and the mixed group-preserving scheme (MGPS) was proposed to solve the inverse Cauchy problem for elliptic equations.
References
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Book
Regularization of Inverse Problems
TL;DR: Inverse problems have been studied in this article, where Tikhonov regularization of nonlinear problems has been applied to weighted polynomial minimization problems, and the Conjugate Gradient Method has been used for numerical realization.
Book
Inverse problems for partial differential equations
TL;DR: Inverse problems and regularization of the Cauchy problem have been studied in this article, with a focus on the uniqueness and stability of the regularization process of the problem.
Book
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications
TL;DR: In this article, the main subject of the author's considerations is coefficient inverse problems, which consist of determining the variable coefficients of a certain differential operator defined in a domain from boundary measurements of a solution or its functionals.
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