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 a two-point boundary value problem for a system of singularly perturbed ordinary differential equations is considered. It is shown that a parameter robust method can be constructed which gives first order convergence in the maximum norm.

A boundary value problem for a fractional power 0 < ε < 1 of the second-order elliptic operator is considered. The boundary value problem is singularly perturbed when ε→ 0. It is solved numerically using a time-dependent problem for a pseudo-parabolic equation. For the auxiliary Cauchy problem, the standard two-level schemes with weights are applied. The numerical results are presented for a mo...

In this paper, we propose an uniformly convergent adaptive finite element method with hybrid basis (AFEM-HB) for the discretization of singularly perturbed nonlinear eigenvalue problems under constraints with applications in Bose-Einstein condensation (BEC) and quantum chemistry. We begin with the time-independent Gross-Pitaevskii equation and show how to reformulate it into a singularly pertur...

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...