In this paper, singularly perturbed quasilinear boundary value problems are taken into account. With purpose, a finite difference scheme is proposed on Shishkin-type mesh (S-mesh). Quasilinearization technique and interpolating quadrature rules used to establish the numerical scheme. Then, an error estimate derived. A experiment demonstratedto verify theory.

We consider a system of two coupled reaction-diffusion equations. When the parameters multiplying the second-order derivatives in the equations are small, their solutions exhibit boundary layers. Moreover, when the parameters are of different magnitudes, two distinct but overlapping boundary layers are present. We study a finite element discretization on general layer-adapted meshes including t...

In this paper, numerical solution for singularly perturbed problem with nonlocal boundary conditions is obtained. Finite difference method used to discretize on the Bakhvalov-Shishkin mesh. The some properties of exact are analyzed. error obtained first-order in discrete maximum norm. Finally, an example solved show advantages finite method.

In this paper we consider the standard bilinear nite element method (FEM) and the corresponding streamline diiusion FEM for the singularly perturbed elliptic boundary value problem ?" (@ 2 u @x 2 + @ 2 u @y 2) ? b(x; y) ru + a (x; y)u = f (x; y) in the two space dimensions. By using the asymptotic expansion method of Vishik and Lyusternik 42] and the technique we used in 25, 26], we prove that ...

A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the θ-scheme as for discontinuous Galerkin in time.

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 objective of this paper is to present a comparative study of fitted-mesh finite difference method, Ritz-Galerkin finite element method and B-spline collocation method for a two-parameter singularly perturbed boundary value problems. Due to the small parameters ε and μ, the boundary layers arise. We have taken a piecewise-uniform fittedmesh to resolve the boundary layers and shown that fitte...

The linear singularly perturbed reaction-diffusion problem is considered. The spline difference scheme on the Shishkin mesh is used to solve the problem numerically. With the special position of collocation points, the obtained scheme satisfies the discrete minimum principle. Numerical experiments which confirm theoretical results are presented. AMS Mathematics Subject Classification (2000): 65...