Using the method of computational experiments on a computer, the effect of the method for calculating the values of the thermal conductivity coefficient at the nodes of the difference grid on the numerical solutions of a one-dimensional nonlinear problem of heat conduction according to explicit and implicit conservative difference schemes is investigated in this article. Thermal conductivity has a power-law relationship with temperature. It is demonstrated that the technique for determining the values of the thermal conductivity coefficient at the nodes of the difference grid affects the accuracy of numerical solutions derived by both the explicit and implicit difference schemes. A approach is suggested for obtaining a numerical solution that is sufficiently near to the analytical solution.
Z. U. Uzakov
Karshi Branch of Tashkent University of Information Technologies Named After Muhammad al-Khorazmi, 180002 Karshi, Beshkent highway, 3d Kilometer, Uzbekistan.
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