A quasi-reversibility regularization method for the Cauchy problem of the Helmholtz equation

DOI10.1080/00207160.2010.482986zbMath1214.35080OpenAlexW1976012069MaRDI QIDQ2995482

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Publication date: 21 April 2011

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2010.482986

zbMATH Keywords

Cauchy problemHelmholtz equationill-posed problemconvergence estimatesquasi-reversibility regularization method

Mathematics Subject Classification ID

Ill-posed problems for PDEs (35R25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Numerical methods for inverse problems for boundary value problems involving PDEs (65N21) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20)

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Cites Work

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• An alternating iterative algorithm for the Cauchy problem associated to the Helmholtz equation
• Fourth-order modified method for the Cauchy problem for the Laplace equation
• Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation
• Boundary knot method for some inverse problems associated with the Helmholtz equation
• A non-local boundary value problem method for the Cauchy problem for elliptic equations
• A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
• Regularization of exponentially ill-posed problems
• Inverse problems for partial differential equations
• An introduction to the mathematical theory of inverse problems

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