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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 57, 2010 - Issue 9
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Original Articles

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

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Pages 691-708 | Received 02 Jun 2009, Accepted 12 Feb 2010, Published online: 04 Jun 2010
 

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.

This work was supported by the Fast Track Project # FT 080007, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

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