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

被引：9
|
作者：
Belonosov, Andrey [1 ]
Shishlenin, Maxim [2 ]
Klyuchinskiy, Dmitriy [1 ]
机构：
[1] Novosibirsk State Univ, Inst Computat Math & Math Geophys, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Sobolev Inst Math, Inst Computat Math & Math Geophys, Novosibirsk 630090, Russia
来源：
ADVANCES IN COMPUTATIONAL MATHEMATICS | 2019年 / 45卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
Parabolic equation; Continuation problem; Numerical methods; Finite-difference scheme inversion; Singular value decomposition; Gradient method;
D O I：
10.1007/s10444-018-9631-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：735 / 755
页数：21
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