Geodesic
Approximate analytic solution of heat conductivity problems with a~mismatch between initial and boundary conditions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 63-71

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We consider a heat conduction problem for an infinite plate with a mismatch between initial and boundary conditions. Using the method of integral relations, we obtain an approximate analytic solution to this problem by determining the temperature perturbation front. The solution has a simple form of an algebraic polynomial without special functions. It allows us to determine the temperature state of the plate in the full range of the Fourier numbers ($0\le\mathsf F\infty$) and is especially effective for very small time intervals.
Keywords: approximate analytic solution, integral relation method, temperature disturbance front
Mots-clés : variable initial condition. 
@article{IVM_2010_4_a6,
     author = {E. V. Stefanyuk and V. A. Kudinov},
     title = {Approximate analytic solution of heat conductivity problems with a~mismatch between initial and boundary conditions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {63--71},
     publisher = {mathdoc},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_4_a6/}
}
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E. V. Stefanyuk; V. A. Kudinov. Approximate analytic solution of heat conductivity problems with a~mismatch between initial and boundary conditions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 4 (2010), pp. 63-71. http://geodesic.mathdoc.fr/item/IVM_2010_4_a6/