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.
Cite this paper
Lee, J. and Kim, D. (2014) Continued Fraction Method for Approximation of Heat Conduction Dynamics in a Semi-Infinite Slab. Applied Mathematics
, 1061-1066. doi: 10.4236/am.2014.57100
 Carslaw, H.S. and Jaeger, J.C. (1989) Conduction of Heat in Solids. Oxford University Press, Oxford.
 Lee, J. and Kim, D.H. (1998) High-Order Approximations for Noncyclic and Cyclic Adsorption in a Particle. Chemical Engineering Science, 53, 1209-1221. http://dx.doi.org/10.1016/S0009-2509(97)00412-0
 Kim, D.H. and Lee, J. (1999) High-Order Approximations for Noncyclic and Cyclic Adsorption in a Biporous Adsorbent. Korean Journal of Chemical Engineering, 16, 69-74.
 Lee, J. and Kim, D.H. (2011) Simple High-Order Approximations for Unsteady-state Diffusion, Adsorption and Reaction in a Catalyst: A Unified Method by a Continued Fraction for Slab, Cylinder and Sphere Geometries. Chemical Engineering Journal, 173, 644-650.
 Lorentzen, L. and Waadeland, H. (1992) Continued Fractions with Applications. Nort-Holland, New York.
 Chen, C.F. and Shieh, L.S. (1969) Continued Fraction Inversion by Routh’s Algorithm. IEEE Transactions on Circuit Theory, 16, 197-202. http://dx.doi.org/10.1109/TCT.1969.1082925
 (2012) Maple, Waterloo Maple Software Inc. www.maplesoft.com
 Zill, D.G. and Cullen, M.R. (1992) Advanced Engineering Mathematics. PWS-KENT Pub., Boston.
 Kailath, T. (1980) Linear Systems. Prentice-Hall, New Jersey.
 Green, M. and Limebeer, D.J.N. (1995) Linear Robust Control. Prentice Hall, New Jersey.
 Finlayson, B.A. (1980) Nonlinear Analysis in Chemical Engineering. MacGraw-Hill, New York.