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 -