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The mollification method and the numerical solution of the inverse heat conduction problem by finite differences

โœ Scribed by D.A. Murio

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
736 KB
Volume
17
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

The inverse heat conduction problem involves the calculation of surface heat flux and/or temperature histories from transient, measured temperatures inside solids. We consider the one dimensional semi-infinite linear case and present a new solution algorithm based on a data filtering interpretation of the mollification method that automatically determines the radius of mollification depending on the amount of noise in the data and finite differences. A fully explicit and stable space marching scheme is developed. We describe several numerical experiments of interest showing that the new procedure is accurate and stable with respect to perturbations in the data even for small dimensionless time steps.

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โœ Hossein Azari; Shuhua Zhang ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 268 KB

## Abstract The aim of this article is to study the parabolic inverse problem of determination of the leading coefficient in the heat equation with an extra condition at the terminal. After introducing a new variable, we reformulate the problem as a nonclassical parabolic equation along with the in