Stability of numerical method of implicit adaptation of transient heat conduction model to rigid body thermophysical parameters

This study is devoted to the analysis of algorithmic stability and complexity of the model of transient heat conductivity with implicit adaptation to the thermophysical parameters of the heated solid body. The implicit adaptation method is based on the substitution of such parameters as heat capacity, thermal conductivity and density in the transient heat conduction equation by two dimensionless adjustable coefficients, uniformly discretized over the entire model lifetime, with their further adjustment using a modified stochastic gradient descent method. In order to ensure the stability of calculations of such a model using a computer, some conditions have been defined in previous studies, which allowed us to obtain stability equal to 64