Modeling a Rotating Circle Thermal Field with a Thermal Source on the Edge

The task of circle heating by a thermal source moving along the circle edge with a constant angular velocity is considered. The circle is a cylinder in which the temperature is the same on each straight line parallel to a cylinder axis, i.e. at each point the temperature is a function of time, distances from a cylinder axis and a polar angle. The computing schemes based on numerical methods are usually used for the similar tasks solution. Explicit schemes solve one equation for each time step of each spatial knot. Implicit schemes solve a system of linear algebraic equations for each time step. The number of equations is connected with the number of spatial knots. In the first case the process is rather simple, but the scheme is not absolutely steady. For this scheme the step order by time should not exceed the square of step order by coordinate. In the second case the scheme is absolutely steady, but it is necessary to solve a complex system of equations, especially for a multidimensional case. The purpose of this work is to use absolutely steady differential-difference explicit scheme based on linear equation application with partial derivatives of the first order which analytical solution (an explicit formula) is known.