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Wavelet and Fourier methods for solving the sideways heat equationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2000 (English)In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 21, no 6, 2187-2205 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2000. Vol. 21, no 6, 2187-2205 p.
##### National Category

Engineering and Technology
##### Identifiers

URN: urn:nbn:se:liu:diva-47660DOI: 10.1137/S1064827597331394OAI: oai:DiVA.org:liu-47660DiVA: diva2:268556
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Available from: 2009-10-11 Created: 2009-10-11 Last updated: 2013-08-30
##### In thesis

We consider an inverse heat conduction problem, the sideways heat equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line *x* = 1, where the solution is wanted for 0 ≤ *x* < 1.

The problem is ill-posed, in the sense that the solution (if it exists) does not depend continuously on the data. We consider stabilizations based on replacing the time derivative in the heat equation by wavelet-based approximations or a Fourier-based approximation. The resulting problem is an initial value problem for an ordinary differential equation, which can be solved by standard numerical methods, e.g., a Runge–Kutta method.

We discuss the numerical implementation of Fourier and wavelet methods for solving the sideways heat equation. Theory predicts that the Fourier method and a method based on Meyer wavelets will give equally good results. Our numerical experiments indicate that also a method based on Daubechies wavelets gives comparable accuracy. As test problems we take model equations with constant and variable coefficients. We also solve a problem from an industrial application with actual measured data.

1. Numerical methods for inverse heat conduction problems$(function(){PrimeFaces.cw("OverlayPanel","overlay255742",{id:"formSmash:j_idt647:0:j_idt651",widgetVar:"overlay255742",target:"formSmash:j_idt647:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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