Geodesic
Explicit scheme for the solution of third boundary value problem for quasi-linear heat equation
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 174-177

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In produced paper numerical method for the solution of third boundary value problem for one-dimensional quasi-linear heat equation grounded on the use of explicit finite-difference scheme is offered. The coefficients’ dependence on temperature is overcome by introducing the new unknown function — a primitive integral of conduction. Test problem with known exact solution for numerical calculations is proposed.
Keywords: thermal conductivity; quasi-linear heat equation; explicit finite-difference schemes; approximation. 
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     author = {M. Z. Khayrislamov and A. V. Herreinstein},
     title = {Explicit scheme for the solution of third boundary value problem for quasi-linear heat equation},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {174--177},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a28/}
}
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M. Z. Khayrislamov; A. V. Herreinstein. Explicit scheme for the solution of third boundary value problem for quasi-linear heat equation. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 5 (2013) no. 2, pp. 174-177. http://geodesic.mathdoc.fr/item/VYURM_2013_5_2_a28/