Exact method to solve 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. solve problems boundary condition first kind on coordinate arbitrary combinations first, second third kinds conditions coordinate, it to use straight lines ordinary sweep coordinate. Approximating matrix built relative functions. Using eigenvalues vectors three-diagonal transition matrix, linear compiled, where coefficients elements eigenvectors matrix. Boundary conditions, initial formed given combination The one-dimensional differential-difference method. From solution, proceed provides order accuracy coordinates. And can be increased using central time. used heat transfer expressed smooth discontinuous non-stationary nature, right-hand side represents moving source outflow heat.