Abstract
The paper presents the possibilities of numerical solution of the non-linear boundary-initial problem described by the Fourier equation. In particular, the equation con- taining the temperature-dependent thermophysical parameters (volumetric specific heat and thermal conductivity) is considered. The problem presented in this paper is connected with the artificial linearization of the task discussed (at the stage of numerical computations), in other words, the new numerical procedure which allows one to remodel the solution ob- tained for linear problem at the time level t t + � to the other solution corresponding to non- linear one. The procedure discussed can be a very effective supplement for different vari- ants of the boundary element method which, as a rule, requires a linear form of the energy equation. In the final part the examples of numerical simulations and the conclusions can be found.
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