The book describes modern methods of differential solution of problems of mathematical physics and related questions of the theory of difference schemes .. The book includes the following sections: homogeneous difference schemes for solving one-dimensional equations of parabolic and hyperbolic types, difference schemes for equations of elliptic type, theory of stability of difference schemes, economical methods for solving multidimensional problems of mathematical physics. Iterative methods for solving differential equations. The book contains a significant number of examples illustrating the main provisions of the theory and contributing to its deeper assimilation. The book is designed for students and graduate students specializing in computational mathematics, as well as for researchers and engineers associated with the numerical solution of problems of mathematical physics.