Numerical solution of the heat conduction problem with memory

It is necessary to use more general models than the classical Fourier heat conduction law describe small-scale thermal processes. The effects of flow memory and capacity (internal energy) in solids are considered first-order integrodifferential evolutionary equations with difference-type kernels. main difficulties applying such nonlocal in-time mathematical associated need work a solution throughout entire history process. paper develops an approach transforming problem into computationally simpler local for system evolution equations. Such transition applicable problems if relaxation functions flux represented as sum exponentials. correctness auxiliary linear ensured by obtained estimates stability concerning initial data right-hand side corresponding Hilbert spaces. study's result prove unconditional proposed two-level scheme weights modeling solid media memory. In this case, finding approximate on new level time not complicated equation. numerical model one-dimensional space presented.