Investigation of the accuracy of an approximate solution of the initial boundary value problem of thermal conductivity with boundary conditions of the third kind

The paper compares two approximations of the solution of the initial boundary value problem of thermal conductivity with boundary conditions of the third kind for the case of a temperature shock of a homogeneous thin plate. A second-order approximation with respect to the plate thickness is obtained. The results of the numerical simulation are compared with the known first-order approximation with respect to the plate thickness. The results obtained demonstrate good convergence. They can be used in controlling the motion of a small spacecraft with elastic structural elements. It is necessary to level out the effect of temperature shock disturbances on the angular motion of a small spacecraft.