Geodesic
Explicit difference scheme for the solution of one-dimensional quasi-linear heat conductivity equation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 1, pp. 12-17

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Numerical method for the solution of the third mixed boundary value problem for one-dimensional quasi-linear heat conductivity equation of a parabolic type based on the use of explicit difference scheme is given. Dependence of coefficients on temperature is overcome by the introduction of the new required function that is a primitive integral of conductivity.
Keywords: thermal conductivity, quasi-linear heat conductivity equation, explicit difference schemes, approximation. 
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     title = {Explicit difference scheme for the solution of one-dimensional quasi-linear heat conductivity equation},
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A. V. Herreinstein; M. Z. Khayrislamov. Explicit difference scheme for the solution of one-dimensional quasi-linear heat conductivity equation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 1, pp. 12-17. http://geodesic.mathdoc.fr/item/VYURM_2013_5_1_a2/