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：10

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

页码：735 / 755

页数：21

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