Algorithm and the numerical solution of the nonlinear mixed heat equation in a Python package

The paper considers a mathematical model for changing the switching modes of an electric arc. Unlike the quasi-stationary thermal mode of amplitude arc combustion, which is well described by the classical parabolic equation of thermal conductivity, in the region of the transition of alternating current through 0, when the arc is switched off by modern switches in a sulfur hexafluoride environment, it is necessary to apply a hyperbolic equation due to the significant non-stationarity of the process. This leads to the formulation of an initial-boundary value problem for a nonlinear hyperbolic-parabolic equation, as well as the need to study it taking into account the nonlinearity of the thermal conductivity coefficient. An algorithm and a program for numerical solution in the widely used Python programming package with visualization in the Matplotlib graphical package and the use of the method of implicit finite-difference schemes for boundary conditions of the first kind have been developed for it.