In this letter, we consider the ultimate boundedness of the singularly perturbed system with measurement noise. The composite controller is commonly used to regulate the singularly perturbed system. However, in the presence of measurement noise, the composite controller does not guarantee the ultimate boundedness of the singularly perturbed system. Thus, we propose the modified composite contro...

This paper presents the application of Differential Quadrature Method (DQM) for finding the numerical solution of singularly perturbed two point singular boundary value problems. The DQM is an efficient discretization technique in solving initial and/or boundary value problems accurately using a considerably small number of grid points. This method is based on the approximation of the derivativ...

Kolmogorov N-widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the N-widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.

We study singularly perturbed linear programs. These are parametric linear programs whose constraints become linearly dependent when the perturbation parameter goes to zero. Problems like that were studied by Jeroslow in 1970’s. He proposed simplex-like method, which works over the field of rational functions. Here we develop an alternative asymptotic simplex method based on Laurent series expa...

In this work, superconvergent approximation of singularly perturbed two-point boundary value problems of reaction-diiusion type and convection-diiusion type are studied. By applying the standard nite element method on the Shishkin mesh, superconvergent error bounds of (N ?1 ln(N +1)) p+1 in a discrete energy norm are established. The error bounds are uniformly valid with respect to the singular...

Such a problem was intensively studied in several works. For example, Ni & Takagi, in [11, 12], show that, for ε sufficiently small, there exists a solution uε of (2) which concentrates in a point Qε ∈ ∂Ω andH(Qε) → max∂ΩH , here H denotes the mean curvature of ∂Ω. Moreover in [10], using the LiapunovSchmidt reduction, Li constructs solutions with single peak and multi-peaks on ∂Ω located near ...

In this paper, we describe a meshless approach to solve singularly perturbed differentialdifference equations of the second order with boundary layer at one end of the interval. In the numerical treatment for such type of problems, first we approximate the terms containing negative and positive shifts which converts it to a singularly perturbed differential equation. Next, a numerical scheme ba...