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 Full article
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Advances in Computational Mathematics
ISSN: 1019-7168 , E-ISSN: 1572-9044 |
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| Output data | Year: 2019, Volume: 45, Number: 2, Pages: 735-755 Pages count : 21 DOI: 10.1007/s10444-018-9631-7 | ||||||
| Tags | Continuation problem; Finite-difference scheme inversion; Gradient method; Numerical methods; Parabolic equation; Singular value decomposition | ||||||
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Abstract:
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. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Cite:
Belonosov A.
, Shishlenin M.
, Klyuchinskiy D.
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
Advances in Computational Mathematics. 2019. V.45. N2. P.735-755. DOI: 10.1007/s10444-018-9631-7 WOS Scopus OpenAlex
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
Advances in Computational Mathematics. 2019. V.45. N2. P.735-755. DOI: 10.1007/s10444-018-9631-7 WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000463858000010 |
| Scopus: | 2-s2.0-85053937998 |
| OpenAlex: | W2893137895 |