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

Andrey Belonosov, Maxim Shishlenin, Dmitriy Klyuchinskiy

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)735-755
Number of pages21
JournalAdvances in Computational Mathematics
Volume45
Issue number2
DOIs
Publication statusPublished - 2 Apr 2019

Keywords

  • Continuation problem
  • Finite-difference scheme inversion
  • Gradient method
  • Numerical methods
  • Parabolic equation
  • Singular value decomposition

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