A computational method for a Cauchy problem of Laplace's equation

DOI10.1016/j.amc.2008.10.063zbMath1160.65049OpenAlexW1984079968MaRDI QIDQ1002306

Ailin Qian, Yu-Jiang Wu

Publication date: 25 February 2009

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2008.10.063

zbMATH Keywords

Fourier transformregularizationCauchy problemerror boundsmethod of linesLaplace equationspectral methodill-posed problem

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs (65M30)

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Cites Work

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• Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation
• A Computational Quasi-Reversibility Method for Cauchy Problems for Laplace’s Equation
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• Stability results for the Cauchy problem for the Laplace equation in a strip
• The Cauchy problem for Laplace's equation via the conjugate gradient method
• A spectral method for solving the sideways heat equation
• Fourier regularization method for solving a Cauchy problem for the Laplace equation

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