[en] The use of finite-difference methods for the solution of partial differential equations is common in both design and research and development because of the advance of computers. The numerical methods for the unsteady heat diffusion equation received most attention not only because of heat transfer problems but also happened to be the basis for any study of parabolic partial differential equations. It is common to test the heat equation first even the methods developed for complex nonlinear parabolic partial differential equations arising in fluid mechanics or convective heat transfer. It is concluded that the finite-element method is conservative in both stability and monoscillation characteristics than the finite-difference method but not as conservative as the method of weighted-residuals. Since the finite-element is unique because of Gurtin's variational principle and numerous finite-differences can be constructed, it is found that some finite-difference schemes are better than the finite-element scheme in accuracy also. Therefore, further attention is focused here on finite-difference schemes only. Various physical problems are considered in the field of heat transfer. These include: numerous problems in steady and unsteady heat conduction; heat pulse problems, such as, plasma torch; problems arising from machining operations, such as, abrasive cut-off and surface grinding. (Auth.)