A new method is introduced for solving free-boundary problems for the heat equation. The method is shown to be uniformly convergent both for first type and nonlinear second type boundary conditions. Approximate solutions are obtained by discretization of the time variable and recursive solution at each time step of classical heat conduction linear problems in slabs of known thickness. An error estimate is given. Numerical tests are presented in a few cases in which exact solutions are known.
An efficient method for solving free-boundary diffusion problems / A. FASANO; PRIMICERIO M.; FONTANELLA F.. - In: MECCANICA. - ISSN 0025-6455. - STAMPA. - 8:(1973), pp. 223-235. [10.1007/BF02342408]
An efficient method for solving free-boundary diffusion problems
FASANO, ANTONIO;PRIMICERIO, MARIO;
1973
Abstract
A new method is introduced for solving free-boundary problems for the heat equation. The method is shown to be uniformly convergent both for first type and nonlinear second type boundary conditions. Approximate solutions are obtained by discretization of the time variable and recursive solution at each time step of classical heat conduction linear problems in slabs of known thickness. An error estimate is given. Numerical tests are presented in a few cases in which exact solutions are known.
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