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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.