An introduction to some recently developed methods for the analysis of systems of singularly perturbed ordinary differential equations is given in the context of a specific problem describing glycolytic oscillations. In suitably scaled variables the governing equations are a planar system of ordinary differential equations depending singularly on two small parameters ε and δ. In [20] it was arg...

The goal of this paper is to study a singular perturbation problem in the framework of optimal control on multi-domains. We consider an optimal control problem in which the controlled system contains a fast and a slow variables. This problem is reformulated as an Hamilton-JacobiBellman (HJB) equation. The main difficulty comes from the fact that the fast variable lives in a multi-domain. The ge...

We design a wavelet optimized finite difference (WOFD) scheme for solving self-adjoint singularly perturbed boundary value problems. The method is based on an interpolating wavelet transform using polynomial interpolation on dyadic grids. Small dissipation of the solution is captured significantly using an adaptive grid. The adaptive feature is performed automatically by thresholding the wavele...

in this paper, we investigate a singular perturbation problem including a fourth order o.d.e. with general linear boundary conditions. firstly, we obtain the necessary conditions of solution of o.d.e. by making use of fundamental solution, then by compatibility of these conditions with boundary conditions, we determine that, for given perturbation problem, whether boundary layer is formed or not.

We give some equivalence estimates on the solution of a singular perturbation problem that represents, among other models, the Koiter and Naghdi shell models. Two of the estimates apply to intermediate shell problems and the third is for membrane/shear dominated shells. From these equivalences, many known and some new sharp estimates on the solutions of the singular perturbation problems easily...

This paper extends the application of Differential Quadrature Method (DQM) for finding the numerical solution of general singularly perturbed two point boundary value problems with a boundary layer at right end point or both end point or at an internal point. The Differential Quadrature Method is an efficient descritization technique in solving initial and /or boundary value problems accurately...

A new spectral Galerkin method is proposed for the convection-dominated convection-diffusion equation. This method employs a new class of trail function spaces. The available error bounds provide a clear theoretical interpretation for the higher accuracy of the new method compared to the conventional spectral methods when applied to problems with thin boundary layers. Efficient solution techniq...

Here N ≥ 1, g(s) ∈ C(R,R) is a function with a subcritical growth, V (x) ∈ C(R ,R) is a positive function and 0 < ε 1. Among solutions of (0.1)ε, we are interested in concentrating families (uε) of solutions, which have the following behavior: (i) uε(x) has a local maximum at xε ∈ R and xε converges to some x0 ∈ R as ε → 0. (ii) rescaled function vε(y) = uε(εy + xε) converges as ε → 0 to a solu...

We consider the following singularly perturbed elliptic problem 2 u ? u + f(u) = 0; u > 0 in ; @u @ + u = 0 on @; where f satisses some growth conditions, 0 +1, and R N (N > 1) is a smooth and bounded domain. The cases = 0 (Neumann problem) and = +1 (Dirichlet problem) have been studied by many authors in recent years. We show that, there exists a generic constant > 1 such that, as ! 0, the lea...