Bu çalışmada, singüler pertürbe Volterra integro-diferansiyel denklemlerin yaklaşık çözümü için nümerik integrasyon yöntemi uygulanır. İlk olarak düzgün bir şebeke üzerinde sonlu fark metodu ile başlanır daha sonra integraller trapez kullanılır. Buradan elde edilen denklem sistemi Thomas algoritması çözülür. Önerilen yöntemin doğruluğunu ve ekonomikliğini ortaya koyan örnek sunulur.

REPORTRAPPORT Discrete approximations for singularly perturbed boundary value problems with parabolic layers Abstract Singularly perturbed boundary value problems for equations of elliptic and parabolic type are studied. For small values of the perturbation parameter, parabolic boundary layers appear in these problems. If classical discretisation methods are used, the solution of the nite diier...

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have one fast variable and an arbitrary number of slow variables, 2) they have a non-hyperbolic singularity of the fold type at the origin. The presence of the a...

In this paper, we have presented a finite difference technique to solve singularly perturbed two-point boundary value problem using deviating argument. We have replaced the given second order boundary value problem by an asymptotically equivalent first order differential equation with deviating argument. We have applied a fourth order finite difference approximation for the first derivative and...

This paper examines the problem of designing an H∞ output feedback controller for a class of nonlinear singularly perturbed systems described by a TakagiSugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop an H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some pre...

In this paper, we proposed a numerical integration method for the solution of singularly perturbed delay differential equation with dual layer behaviour. In this method, an asymptotically equivalent first order neutral type delay differential equation is obtained from the second order singularly perturbed delay differential equation and employed Trapezoidal rule on it. Then, linear interpolatio...

This paper is concerned with a class of singularly perturbed systems of two conservation laws. A small perturbation parameter is introduced in the dynamics and the boundary conditions. By setting the perturbation parameter to zero, the singularly perturbed system of conservation laws can be treated as two subsystems of one conservation law: the reduced system and the boundary-layer system. The ...

The derivatives of the solution of singularly perturbed diierential equations become unbounded as the singular perturbation parameter " tends to zero. Therefore to approximate such derivatives, it is required to scale the derivatives in such a way that they are of order one for all values of the perturbation parameter. In practice , derivatives are related to the ux or drag and, hence, it is de...

Abstract – In this paper we present a unified approach for optimal control and filtering of linear continuous-time singularly perturbed linear systems that facilitates complete and exact decomposition of optimal control and filtering tasks into pure-slow and pure-fast time scales. The presented methodology eliminates numerical ill-conditioning of the original singularly perturbed problems, intr...