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 -