The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the meth...

Abstract An extended second order finite difference method on a variable mesh is proposed for the solution of singularly perturbed boundary value problem. A discrete equation achieved non uniform by extending first and derivatives to higher differences. This solved efficiently using tridiagonal solver. The analysed convergence, convergence derived. Model examples are scheme compared with availa...

Ionic channels and semiconductor devices use atomic scale structures to control macroscopic flows from one reservoir to another. The onedimensional steady-state Poisson-Nernst-Planck (PNP) system is a useful representation of these devices but experience shows that describing the reservoirs as boundary conditions is difficult. We study the PNP system for two types of ions with three regions of ...

A collection of typical examples shows the exotic behaviour of numerical methods when applied to singular perturbation problems. While standard meshes are used in the first six examples, even on layer-adapted meshes several surprising phenomena are shown to occur. AMS subject classification (2000): 35 L10, 35 L12, 35 L60

A singularly perturbed time-dependent convection-diffusion problem is examined on non-rectangular domains. The nature of the boundary and interior layers that arise depends on the geometry of the domains. For problems with different types of layers, various numerical methods are constructed to resolve the layers in the solutions and the numerical solutions are shown to converge independently of...

The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge-Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed. AMS Subject Classification: 65L05

Nonlinear singularly perturbed interior layer problems are examined. Numerical results are presented for a numerical method consisting of a monotone scheme on a Shishkin mesh refined around the approximate location of the interior layer. keywords: Singular Perturbation, Shishkin mesh, Nonlinear, Interior Layer

We derive a closed form expression for the Green function of linear evolution equation with the Dirichlet boundary condition for an arbitrary region, based on singular perturbation approach to boundary problems. PACS numbers: 03.65.-w, 03.65.Ge, 02.90.+p Published in Journal of Physics A: Mathematical and General Vol. 32 (1999) 1261-1267 e–mails: [email protected], [email protected] 1