A two-stage LGSM to identify time-dependent heat source through an internal measurement of temperature

✍ Scribed by Chein-Shan Liu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 233 KB
• Volume: 52
• Category: Article
• ISSN: 0017-9310
• DOI: 10.1016/j.ijheatmasstransfer.2008.09.021

✦ Synopsis

a b s t r a c t

We consider an inverse problem for estimating an unknown time-dependent heat source HðtÞ in a heat conduction equation T t ðx; tÞ ¼ T xx ðx; tÞ þ HðtÞ, with the aid of an extra measurement of temperature at an internal point. The Lie-group shooting method (LGSM) was used in the solution of this inverse problem; however, when the data are acquired at an internal point we require to develop a two-stage Lie-group shooting method (TSLGSM) to solve it. This novel approach is examined through numerical examples to convince that it is a rather accurate and efficient method, whose estimation error is small even for the identification of discontinuous and oscillatory heat source under large noise.