We study the initial value problem of a singularly perturbed first order ordinary differential equation in case that the degenerate equation has a double root. We construct the formal asymptotic expansion of the solution such that the boundary layer functions decay exponentially. This requires a modification of the standard procedure. The asymptotic solution will be used to construct lower 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...

A numerical method based on finite difference method with variable mesh is given for self-adjoint singularly perturbed two-point boundary value problems. To obtain parameteruniform convergence, a variable mesh is constructed, which is dense in the boundary layer region and coarse in the outer region. The uniform convergence analysis of the method is discussed. The original problem is reduced to...

In this paper, a new algorithm is presented to approximate the solution of a singularly perturbed boundary value problem with leftlayer based on the homotopy perturbation technique and applying the Laplace transformation. The convergence theorem and the error bound of the proposed method are proved. The method is examined by solving two examples. The results demonstrate the reliability and effi...

{ We consider the bilinear nite element method on a Shishkin mesh for the singularly perturbed elliptic boundary value problem ?" 2 (@ 2 u @x 2 + @ 2 u @y 2) + a(x; y)u = f(x; y) in two space dimensions. By using a very sophisticated asymptotic expansion of Han et al. 11] and the technique we used in 17], we prove that our method achieves almost second-order uniform convergence rate in L 2-norm...

In this research, the numerical integral method procedure on uniform mesh is used to solve singularly perturbed problem which has boundary value. This also includes trapezoid method, finite difference and Thomas algorithm. The converted by using approximations method. Finally, convergence of presented analyzed through sample application. Thus, correctness sufficiency are shown.