 This paper studies the characterization of the stability boundary (the topological boundary of stability region) of nonlinear autonomous singularly perturbed dynamical systems. In particular, a relationship between the stability boundary of the singularly perturbed system and the stability boundary and stability region of the slow and fast systems is investigated. Conditions, in terms of loca...

in this paper, we have proposed a numerical method for singularly perturbed  fourth order ordinary differential equations of convection-diffusion type. the numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and  finite difference method. in order to get a numerical solution for the derivative of the solution, the given interval is divided  in...

The numerical solution of a linear singularly-perturbed reaction-diffusion two-point boundary value problem is considered. The method used is adaptive movement of a fixed number of mesh points by equidistribution of a user-chosen monitor function. A partly heuristic argument based on truncation error analysis leads to several suitable monitor functions, but also shows that the standard arc-leng...

In this work, a singularly perturbed two-point boundary value problem of convection-diiusion type is considered. A hp version nite element method on a strongly graded piecewise uniform mesh of Shishkin type is used to solve the model problem. With the analytic assumption of the input data, it is shown that the method converges exponentially and the convergence is uniformly valid with respect to...

A singularly perturbed semilinear two point boundary value problem is considered, without any restriction on its turning points. A difference scheme is presented for solving this problem on an arbitrary locally quasiuniform mesh. It is shown that the solution of the scheme is first order accurate, uniformly in the perturbation parameter, in a discrete L1 norm. Numerical results are presented fo...

In the present paper, a numerical algorithm using fifth degree quintic B-spline for fourth order singular perturbation problem has been developed. The most of the numerical methods used for higher order singularly perturbed boundary value problems transform the problems into equivalent system of first and/or second order differential equations. However, in the present method, fifth degree B-spl...

In this paper, a new initial value method for solving a class of nonlinear singularly perturbed boundary value problems with a boundary layer at one end is proposed. The method is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). Using singular perturbation anal...