Аннотация:The equations of mathematical physics, which describe some actual processes, are defined on manifolds (tangent, a companying or others) that are not integrable.The derivatives on such manifolds turn out to be inconsistent, i.e. they don’t form a differential. The solutions to equations obtained in numerical modelling the derivatives on such manifolds are not func-tions. They will depend on the commutator made up by noncommutative mixed derivatives, and this fact relates to inconsistence of derivatives. The exact solutions (functions) to the equations of mathematical physics are obtained only in the case when the integrable structu-res are realized. So called generalized solutions are solutions on integrable struc- tures. They are functions (depend only on variables) but are defined only on integrable structure, and, hence, the derivatives of functions or the functions themselves have discon-tinuities in the direction normal to integrable structure. In numerical simulation of the derivatives of differential equations, one cannot obtain such generalized solutions by con- tinuous way, since this is connected with going from initial nonintegrable manifold to inte-grable structures. In numerical solving the equations of mathematical physics, it is possible to obtain exact solutions to differential equations only with the help of additio-nal methods.