Method of decreasing the order of partial differential equation by reducing to two ordinary differential equation

Using additional sought-for functions and additional boundary conditions in integral method of heat balance, we obtain high-accuracy approximate analytic solutions to non-stationary heat conductivity problem for infinite solid cylinder that allow to estimate a temperature state practically in all time range of non-stationary process. The heat conducting process is divided into two stages with respect to time. The initial problem for equation in partial derivatives is represented in the form of two problems, in which the integration is performed over ordinary differential equations with respect to respective additional sought-for functions. This method allows to simplify substantially the process of solving the initial problem by reducing it to sequentially solving two problems, in which of them they use additional boundary conditions.