Standard

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. / Belonosov, Andrey; Shishlenin, Maxim; Klyuchinskiy, Dmitriy.

в: Advances in Computational Mathematics, Том 45, № 2, 02.04.2019, стр. 735-755.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Belonosov, A, Shishlenin, M & Klyuchinskiy, D 2019, '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, Том. 45, № 2, стр. 735-755. https://doi.org/10.1007/s10444-018-9631-7

APA

Belonosov, A., Shishlenin, M., & Klyuchinskiy, D. (2019). 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, 45(2), 735-755. https://doi.org/10.1007/s10444-018-9631-7

Vancouver

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 апр. 2;45(2):735-755. doi: 10.1007/s10444-018-9631-7

Author

Belonosov, Andrey ; Shishlenin, Maxim ; Klyuchinskiy, Dmitriy. / 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. в: Advances in Computational Mathematics. 2019 ; Том 45, № 2. стр. 735-755.

BibTeX

@article{97e20f49588140c599ac7bf51aa72a3c,
title = "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",
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.",
keywords = "Continuation problem, Finite-difference scheme inversion, Gradient method, Numerical methods, Parabolic equation, Singular value decomposition",
author = "Andrey Belonosov and Maxim Shishlenin and Dmitriy Klyuchinskiy",
year = "2019",
month = apr,
day = "2",
doi = "10.1007/s10444-018-9631-7",
language = "English",
volume = "45",
pages = "735--755",
journal = "Advances in Computational Mathematics",
issn = "1019-7168",
publisher = "Springer Netherlands",
number = "2",

}

RIS

TY - JOUR

T1 - 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

AU - Belonosov, Andrey

AU - Shishlenin, Maxim

AU - Klyuchinskiy, Dmitriy

PY - 2019/4/2

Y1 - 2019/4/2

N2 - 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.

AB - 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.

KW - Continuation problem

KW - Finite-difference scheme inversion

KW - Gradient method

KW - Numerical methods

KW - Parabolic equation

KW - Singular value decomposition

UR - http://www.scopus.com/inward/record.url?scp=85053937998&partnerID=8YFLogxK

U2 - 10.1007/s10444-018-9631-7

DO - 10.1007/s10444-018-9631-7

M3 - Article

AN - SCOPUS:85053937998

VL - 45

SP - 735

EP - 755

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

IS - 2

ER -

ID: 16749061