Solution of the Initial Inverse Problems in the Heat Equation Using the Finite Difference Method with Positivity-Preserving Padé Schemes

The classical inverse problem of recovering the initial temperature distribution from the final temperature distribution is extremely ill-posed. We propose a class of numerical schemes based on positivity-preserving Padé approximations to solve initial inverse problems in the heat equation. We also...

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Bibliographic Details
Published in:Numerical heat transfer. Part A, Applications Vol. 57; no. 9; pp. 691 - 708
Main Authors: Masood, K., Yousuf, M.
Format: Journal Article
Language:English
Published: Philadelphia Taylor & Francis Group 03.06.2010
Taylor & Francis Ltd
Subjects:
Approximation
Finite difference method
Heat equations
Heat transfer
Inverse problems
Mathematical analysis
Mathematical models
Numerical analysis
Pade approximation
Recovering
Temperature
Temperature distribution
ISSN:1040-7782, 1521-0634
Online Access:Get full text
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Summary:The classical inverse problem of recovering the initial temperature distribution from the final temperature distribution is extremely ill-posed. We propose a class of numerical schemes based on positivity-preserving Padé approximations to solve initial inverse problems in the heat equation. We also utilize a partial fraction decomposition technique to solve the problem more efficiently when higher order Padé approximations are used. We apply the proposed numerical schemes on the parabolic heat equation. Our aim is to model the problem as a direct problem and use our numerical schemes to recover the initial profile in a stable and efficient way.
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ISSN:1040-7782
1521-0634
DOI:10.1080/10407781003744763