Existence of a solution of an initial-boundary value difference problem for a linear heat equation with a nonlinear boundary condition

A problem of heat propagation in the ground from a heated pipeline with a partially heat-insulating shell is considered. The possibility is proved to construct a numerical solution of a linear heat equation by using a direct finite-difference method in the case when the thermal radiation on the ground surface is taken into account. On the basis of the theorem about the solvability of a system of linear difference equations by means of the sweep method, the existence and uniqueness of a solution of a corresponding difference problem with nonlinear boundary condition are proved.