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Identification of temperature‐dependent thermophysical properties in a partial differential equation subject to extra final measurement data
Author(s) -
Liu CheinShan
Publication year - 2007
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20211
Subject(s) - mathematics , partial differential equation , partial derivative , a priori and a posteriori , heat capacity , heat equation , thermal conductivity , first order partial differential equation , inverse problem , volumetric heat capacity , parabolic partial differential equation , noise (video) , mathematical analysis , thermodynamics , heat transfer , heat transfer coefficient , computer science , physics , philosophy , epistemology , artificial intelligence , image (mathematics)
Abstract We consider an inverse problem for estimating the two coefficient functions c and k in a parabolic type partial differential equation c ( u ) u t = ∂ [ k ( u ) u x ]/∂ x with the aid of the measurements of u at two different times. The first‐ and second‐order one‐step group preserving schemes are developed. Solving the resultant algebraic equations with a closed‐form, we can estimate the unknown temperature‐dependent thermal conductivity and heat capacity. The new methods possess threefold advantages: they do not require any a priori information on the functional forms of thermal conductivity and heat capacity; no initial guesses are required; and no iterations are required. Numerical examples are examined to show that the new approaches have high accuracy and efficiency, even there are rare measured data. When the measured temperatures are polluted by uniform or normal random noise, the estimated results are also good. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007