In this paper, we present a numerical integration method to solve singularly perturbed delay differential equations. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the numerical integration. Then, linear interpolation is used to get three term recurrence relation which is solve...

We study the singularly perturbed (sixth-order) Boussinesq equation recently introduced by Daripa and Hua [Appl. Math. Comput. 101 (1999), 159-207]. This equation describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Bond number less than but very close to 1/3. On the basis of far-field analyses and heuristic arguments, ...

Boundary equilibria bifurcation (BEB) arises in piecewise-smooth (PWS) systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to arising singular perturbation problems which limit as some ? 0 PWS undergo BEB. This work completes classification for codimension-1 singularly the plane initiated by present authors [19], using combina...

This paper considers the robust control problem for nonstandard singularly perturbed systems with time-varying norm-bounded parameter uncertainties in state equations. In order to obtain the controller such that both robust stability and a disturbance attenuation level larger than a arbitrary boundary value are achieved, irrespective of uncertainties, we must solve algebraic Riccati equation wi...

This paper deals with the singularly perturbed boundary value problem for a linear second order differential-difference equation of the convection-diffusion type with small delay parameter. A fourth order finite difference method is developed for solving singularly perturbed differential difference equations. To handle the delay argument, we construct a special type of mesh, so that the term co...