Decomposition Method And Stability For Some Singular Perturbation Problems

In this paper,we investigate a decomposition method for systems of large dimension differential equations and stability of certain classes of singular perturbation problems.The decomposition method allows us to reduce the difficulties in solving complex singularly perturbed systems.At the same time,the accuracy of the results remains quite high.For clarity,the decomposition method is applied to the mathematical model of virus spread in the herd.The existence of an integral manifold is proved,the first and second approximations are constructed and the results of the decomposition method application are analyzed.Another object of the study is the stability of singularly perturbed discontinuous problems at some point.In this paper we construct representations for eigenvalues and eigenfunctions.Based on their construction,we have determined the conditions under which this task will be stable.