A comparative analysis of numerical methods of solving the continuation problem for 1D parabolic equation with the data given on the part of the boundary
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The ill-posed continuation problem for the one-dimensional parabolic equation with the data given on the part of the boundary is investigated. We prove the uniqueness theorem about the solution of the continuation problem. The finite-difference scheme inversion, the singular value decomposition, and gradient type method are numerically compared. The influence of a noisy data on the solution is presented.
KeywordsParabolic equation Continuation problem Numerical methods Finite-difference scheme inversion Singular value decomposition Gradient method
Mathematics Subject Classification (2010)65M32 49N45 35K35
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Authors kindly thank Professor Michael V. Klibanov for very careful remarks and comments which significantly helped us to improve the article.
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