Analysis of systems of singular ordinary differential equations
Systems of ordinary differential equations with a small parameter at the derivative and specific features of the construction of their periodic solutions are considered. Sufficient conditions for the existence and uniqueness of such a periodic solution is presented. An iterative procedure of the construction of the steady-state of a system of differential equations with a small parameter at the derivative is proposed. This iterative procedure is reduced to the solution of a system of nonlinear algebraic equations and does not involve the integration of the system of differential equations. The problem of numerical approximation of the solution is considered based on the proposed procedure. Some sources of possible divergence of this procedure are found and sufficient conditions for the convergence of the proposed procedure are proved. The results of some numerical experiments are presented and compared with the results of the theory.
systems of singular ordinary differential equations
scientific article; zbMATH DE number 1505749