In this paper, we study the tracking control problem for a nonlinear system in which the zero dynamics may be unstable. The objective here is to approximate the nonlinear system by another singularly perturbed system by using a small singular perturbation parameter  . The proposed approach is based on the methodology of exact input output linearization control, the integrator backstepping appr...

We consider the following singularly perturbed elliptic problem: ε∆u = (u− a(y)) (u− b(y)) in Ω, ∂u

Singularly perturbed boundary value problem can be solved using various techniques. The solution of the following fourth order self adjoint singularly perturbed boundary value problem is approximated using quintic spline Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(1)(a) = α2, y(1)(b) = α3, } or Ly = − y(4) + p(x)y = f(x), p(x) ≥ p > 0, y(a) = α0, y(b) = α1, y(2)(a) = α4, y...

We consider the finite element approximation of the solution to a singularly perturbed second order differential equation with a constant delay. The boundary value problem can be cast as a singularly perturbed transmission problem, whose solution may be decomposed into a smooth part, a boundary layer part, an interior/interface layer part and a remainder. Upon discussing the regularity of each ...

Numerical approximations to the solution of a linear singularly perturbed parabolic problem are generated using a backward Euler method in time and an upwinded finite difference operator in space on a piecewise-uniform Shishkin mesh for a convectiondiffusion problem. A proof is given to show first order convergence of these numerical approximations in appropriately weighted C-norm. Numerical re...