boundary value problem

Effective algorithm of calculating the static modes of nonlinear electromagnetic circuits

Existing electromagnetic circuits are mostly non-linear, however known methods of analysis of the processes for those circuits do not meet modern requirements and it is the one of least developed parts of Theoretical Electric Engineering. Therefore the development of methods of analysis is an important issue. The article discusses the problem of developing the algorithm of calculation for static modes in nonlinear electromagnetic circuits with reactive elements under the influence of periodical disturbances.

Exact difference scheme for system nonlinear ODEs of second order on semi-infinite intervals

We constructed and substantiated the exact three-point differential scheme for the numerical solution of boundary value problems on a semi-infinite interval for systems of second order nonlinear ordinary differential equations with non-selfadjoint operator.  The existence and uniqueness of the solution of the exact three-point difference scheme and the convergence of the method of successive approximations for its findings are proved under the conditions of existence and uniqueness of the solution of the  boundary value problem.