Exact method to solve finite difference equations of linear heat transfer problems

When approximating multidimensional partial differential equations, the values of grid functions from neighboring layers are taken previous time layer or approximation. As a result, along with approximation discrepancy, an additional discrepancy numerical solution is formed. To reduce this when solving stationary elliptic equation, parabolization carried out and resulting equation solved by method successive approximations. This eliminated in approximate analytical proposed below for two- dimensional equations parabolic types, exact system finite difference fixed obtained. Boundary conditions, initial formed given combination functions. The one-dimensional differential-difference ordinary sweep method. From solution, proceed to provides second order accuracy on coordinates. And can be increased using central time. used solve heat transfer problems, boundary conditions expressed smooth discontinuous non-stationary nature, right-hand side represents moving source outflow heat.