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Numerical solution to a sideways parabolic equation
Author(s) -
Hào Dinh Nho,
Reinhardt H.J.,
Schneider A.
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010220)50:5<1253::aid-nme81>3.0.co;2-6
Subject(s) - mathematics , thermal conduction , plane (geometry) , parabolic partial differential equation , heat equation , inverse problem , mathematical analysis , geometry , partial differential equation , physics , thermodynamics
The inverse heat conduction problem can be considered to be a sideways parabolic equation in the quarter plane. This is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but one side is inaccessible to measurements. A numerical procedure for this severely ill‐posed problem is suggested, which consists of two steps, namely a mollification of the data and a marching difference scheme. The numerical method is proved to be stable. Several computational results are presented and discussed. Copyright © 2001 John Wiley & Sons, Ltd.