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Hybrid Laplace transform/finite difference method for transient heat conduction problems
Author(s) -
Chen HanTaw,
Chen Cha'OKuang
Publication year - 1988
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620260613
Subject(s) - laplace transform applied to differential equations , laplace transform , two sided laplace transform , inverse laplace transform , mathematics , green's function for the three variable laplace equation , finite element method , laplace's equation , mathematical analysis , finite difference method , finite difference , partial differential equation , laplace–stieltjes transform , finite difference coefficient , transient (computer programming) , heat equation , thermal conduction , integral transform , mixed finite element method , computer science , physics , thermodynamics , fourier transform , fractional fourier transform , fourier analysis , operating system
The new method involving the combined use of the Laplace transform and the finite difference method is applicable to the problem of time‐dependent heat flow systems. The present method removes the time derivatives from the governing differential equation using the Laplace transform and then solves the associated equation with the finite difference method. The transformed temperature is inverted numerically by the method of Honig and Hirdes to obtain the result in the physical quantities. The present results are compared in tables with exact solutions and those obtained from the combined use of the Laplace transform and the finite element method. It is found that the present method is reliable and efficient.