Numerical Modeling of Nonlinear Parabolic Type Differential Equation

In this article, the boundary value problem posed for a one-dimensional quasilinear heat transfer equation of a nonlinear parabolic type is numerically modeled using an explicit separation scheme. The heat transfer coefficient is taken as proportional to temperature: k(u)  u The initial temperature distribution is parabolic, and the temperature at the boundaries is assumed to be zero. The stability condition of the separation scheme obtained as a result of discretization is determined and an example of calculation for one time step is given. The proposed method is simple nonlinear parabolic equation, quasilinear heat transfer, explicit