In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It ...

in this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer. a fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. thomas algorithm is used to solve the tri-diagonal system. the stability of the algorithm is investigated. it ...

We consider singularly perturbed reaction-diffusion equations with singularly perturbed Neumann boundary conditions. We establish the existence of a time-periodic solution u(x, t, ε) with boundary layers and derive conditions for their asymptotic stability The boundary layer part of u(x, t, ε) is of order one, which distinguishes our case from the case of regularly perturbed Neumann boundary co...

In this paper, we presented an asymptotic fitted approach to solve singularly perturbed delay differential equations of second order with left and right boundary. In this approach, the singularly perturbed delay differential equations is modified by approximating the term containing negative shift using Taylor series expansion. After approximating the coefficient of the second derivative of the...

In this paper, a numerical method named as Initial Value Technique (IVT) is suggested to solve singularly perturbed boundary value problems for second order ordinary differential equations of reactiondiffusion type with a delay (negative shift). In this technique, the original problem of solving the second order differential equation is reduced to solving four first order singularly perturbed d...

The aim of the paper is to describe the main critical cases in the theory of singularly perturbed optimal control problems and to give examples which are typical for slow/fast systems. The theory has traditionally dealt only with perturbation problems near normally hyperbolic manifold of singularities and this manifold is supposed to isolated. We reduce the original singularly perturbed problem...

Abstract In this paper, we have developed a fifth order compact difference method for a class of singularly perturbed singular two-point boundary value problems. To avoid the singularity at zero a terminal boundary condition in the implicit form is derived. Using this condition as one of the boundary condition we solve the singularly perturbed singular two-point boundary value problem by the fi...