Solution of the initial inverse problems in the heat equation using the finite difference method with positivity-preserving pade schemes

K. Masood; M. Yousuf

doi:10.1080/10407781003744763

Solution of the initial inverse problems in the heat equation using the finite difference method with positivity-preserving pade schemes

K. Masood, M. Yousuf^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	691-708
Number of pages	18
Journal	Numerical Heat Transfer; Part A: Applications
Volume	57
Issue number	9
DOIs	https://doi.org/10.1080/10407781003744763
State	Published - Jan 2010

Bibliographical note

Funding Information:
Received 2 June 2009; accepted 12 February 2010. This work was supported by the Fast Track Project # FT 080007, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Address correspondence to M. Yousuf, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. E-mail: [email protected]

ASJC Scopus subject areas

Numerical Analysis
Condensed Matter Physics

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title = "Solution of the initial inverse problems in the heat equation using the finite difference method with positivity-preserving pade schemes",

abstract = "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 Pad{\'e} 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 Pad{\'e} 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.",

author = "K. Masood and M. Yousuf",

note = "Funding Information: Received 2 June 2009; accepted 12 February 2010. This work was supported by the Fast Track Project \# FT 080007, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. Address correspondence to M. Yousuf, Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia. E-mail: [email protected]",

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N2 - 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.

AB - 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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IS - 9

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Solution of the initial inverse problems in the heat equation using the finite difference method with positivity-preserving pade schemes

Abstract

Bibliographical note

ASJC Scopus subject areas

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