We consider a spline difference scheme on a piecewise uniform Shishkin mesh for a singularly perturbed boundary value problem with two parameters. We show that the discrete minimum principle holds for a suitably chosen collocation points. Furthermore, bounds on the discrete counterparts of the layer functions are given. Numerical results indicate uniform convergence. AMS Mathematics Subject Cla...

Second order elliptic boundary value problems which are allowed to degenerate into zero order equations are considered. The behavior of the ordinary Galerkin finite element method without special arrangements to treat singularities is studied as the problem ranges from true second order to singularly perturbed.

A fourth-order finite-difference method for a semilinear singularly perturbed boundary value problem is studied. This method is based on Hermitian approximation of the second derivative on special new discretization mesh of Bakhvalov type. Numerical examples which demonstrate the effectiveness of the method are presented. AMS Mathematics Subject Classification (2000): 65L10

In this paper the fourth order singularly perturbed boundary value problem is solved using septic spline. The given method is proved to be fourth order convergent. To illustrate the efficiency of the method two examples are considered. The method is also compared with the existing method and it is evident that the method is better than the existing one. MSC: 65L10

© journal de afrikana www.jdeafrikana.com 233 Original Research Article ISSN; 2411-1376 Title: Uniformly Convergent Second Order Completely Fitted Finite Difference Scheme for Two-Parameters Singularly Perturbed Two Point Boundary Value Problem K. Phaneendra*, G. Mahesh Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, India _____________________...

The singularly perturbed parabolic boundary value problem is considered. Difference scheme is obtained by using cubic spline difference scheme on Shishkin’s mesh in space and classical discretization on uniform mesh in time. To obtain better stability and simpler matrix the fitting factor in polynomial form is used. The uniform convergence is achieved. Numerical results are presented. AMS Mathe...

We consider a non-standard nonlinear singularly perturbed 2D initial-boundary value problem with Venttsel type boundary conditions, arising in homogenization of radiative-conductive heat transfer problems. establish existence, uniqueness and regularity weak solution v. obtained estimates for the derivatives Dtv, D12v, D22v, D1D2v qualified order small parameter ε.

The aim of this study is to develop a regularization method for boundary value problems parabolic equation. A singularly perturbed problem on the semiaxis considered in case “simple” rational turning point. To prove asymptotic convergence series, maximum principle used.