| Summary: | 碩士 === 國立臺灣海洋大學 === 機械與機電工程學系 === 95 === In this paper we are applying the LGEM to estimate the unknown parameters from bio-heat transfer equation and optical propagation equation.
It is composed of two parts. First, we discuss PDE of bio-heat transfer equation. The semi-discrete procedure of PDE yields n coupled system of ODEs, and then transform them into the Minkowskian type ODEs. By adding initial and final temperature, we solve adaptive factor by one-step GPS, Substituting the solved adaptive factor into the non-linear equations, we can obtain thermal conductivity and thermal capacity.
In the second part, we use a good idea to solve the estimation problem. We will multiply into the ODE of optical propagation equation, such that we have a PDE. The semi-discrete procedure of PDE yields n coupled system of ODEs, and then transform them into the Minkowskian type ODEs. By adding initial and final temperature, we can solve the obtain adaptive factor by one-step GPS, inserting which into the non-linear equation, we can obtain optical diffusion and optical absorption coefficients of tissue.
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