This computational study investigates a class of singularly perturbed second-order boundary-value problems having dual (twin) boundary layers and simple turning points. It is well-known that the classical discretization methods fail to resolve sharp gradients arising in solving differential equations as perturbation (diffusion) parameter decreases, i.e., ε → 0+. To this end, paper proposes semi...

A linear singularly perturbed interior turning point problem with a continuous convection coefficient is examined in this paper. Parameter uniform numerical methods composed of monotone finite difference operators and piecewise-uniform Shishkin meshes, are constructed and analysed for this class of problems. A refined Shishkin mesh is placed around the location of the interior layer and we cons...

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 ...

The aim of this paper is to present a numerical method for singularly perturbed convection-diffusion problems with a delay. The method is a combination of the asymptotic expansion technique and the reproducing kernel method (RKM). First an asymptotic expansion for the solution of the given singularly perturbed delayed boundary value problem is constructed. Then the reduced regular delayed diffe...

A singularly perturbed boundary-value problem with a multiple turning point at a boundary is considered. A representation of the solution is given, and it is used in the construction of a uniform finite-difference scheme. The scheme is a fiNJt-order exponentially fitted one. An improved modification on a special discretization mesh is given.