An Effective Analytical Algorithm For Several Singular Perturbation Differential Systems

Singularly perturbation theory and method is a very active and expanding discipline. Aswe known, singular perturbation problems arise very frequently in the fields of appliedmathematics and engineering applications (such as biochemical kinetics, genetics, plasmaphysics and mechanical) which also have become an important area of investigation. In thispaper, by the theory of asymptotic expansion and matched asymptotic expansion, we solvedifferential equations. On the basis of existing research, we discuss a class of singularperturbed system.In the chapter1, the research background and common methods of singular perturbationare introduced.In the chapter2, an iterative method is illustrated for solving a class of singular perturbedslow-fast system including three differential equations. By some techniques, we not only givean error accuracy by differential inequality but also present an error estimate formula.In the chapter3, the perturbed solution of boundary value problem for slow-fast system isinvestigated. Specifically, this paper present several common slow-fast systems. After a seriesof deformation, we can get linear equation with a small parameter. Thereby, we can use avariety of perturbation methods, such as regular perturbation method, WKB method to gettheir general solution.In the chapter4, the boundary layer problems for a class of second-order nonlinearordinary differential equations with variable coefficients are investigated. The position ofboundary layer is determined and the asymptotic solution is given by using the matchingmethod.