Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi-Infinite Slab

Jietae Lee, Dong Hyun Kim

Department of Chemical Engineering, Kyungpook National University, Taegu, South Korea.

DOI: 10.4236/am.2014.57100                

Abstract

Heat conduction dynamics are described by partial differential equations. Their approximations with a set of finite number of ordinary differential equations are often required for simpler computations and analyses. Rational approximations of the Laplace solutions such as the Pade approximation can be used for this purpose. For some heat conduction problems appearing in a semi-infinite slab, however, such rational approximations are not easy to obtain because the Laplace solutions are not analytic at the origin. In this article, a continued fraction method has been proposed to obtain rational approximations of such heat conduction dynamics in a semi-infinite slab.

Keywords

Heat Conduction Dynamics, Semi-Infinite Slab, Continued Fraction, Pade Approximation

Conflicts of Interest

The authors declare no conflicts of interest.

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