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.

In: Advances in Computational Mathematics, Vol. 45, No. 2, 02.04.2019, p. 735-755.

Research output: Contribution to journal › Article › peer-review

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, vol. 45, no. 2, pp. 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 Apr 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. In: Advances in Computational Mathematics. 2019 ; Vol. 45, No. 2. pp. 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