Uniform convergence difference schemes for singularly perturbed mixed boundary problems
نویسندگان
چکیده
منابع مشابه
A Parameter Uniform Numerical Scheme for Singularly Perturbed Differential-difference Equations with Mixed Shifts
In this paper, we consider a second-order singularly perturbed differential-difference equations with mixed delay and advance parameters. At first, we approximate the model problem by an upwind finite difference scheme on a Shishkin mesh. We know that the upwind scheme is stable and its solution is oscillation free, but it gives lower order of accuracy. So, to increase the convergence, we propo...
متن کاملUniform High-Order Difference Schemes for a Singularly Perturbed Two-Point Boundary Value Problem
A family of uniformly accurate finite-difference schemes for the model problem -em" + a(x)u' + b(x)u = f(x) is constructed using a general finite-difference framework of Lynch and Rice [Math. Comp., v. 34, 1980, pp. 333-372] and Doedel [SIAM J. Numer. Anal., v. 15, 1978, pp. 450-465], A scheme of order hp (uniform in e) is constructed to be exact on a collection of functions of the type {1, x,....
متن کاملParameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems
In this paper, parameter-uniform numerical methods for a class of singularly perturbed parabolic partial differential equations with two small parameters on a rectangular domain are studied. Parameter-explicit theoretical bounds on the derivatives of the solutions are derived. The solution is decomposed into a sum of regular and singular components. A numerical algorithm based on an upwind fini...
متن کاملGraded - Mesh Difference Schemes for Singularly Perturbed Two - Point Boundary Value Problems * By Eugene
This paper is concerned with the numerical approximation by compact finitedifference schemes of differential operators of the form Leu = eu(m) + ^Jv=0 avv^ without turning points. The stability of L£ combined with various auxiliary conditions is discussed, and a representation result for solutions of problems involving it is proven. This representation decomposes the solution into a smooth oute...
متن کاملThe " { uniform convergence of the discretederivativesfor singularly perturbed problems
The derivatives of the solution of singularly perturbed diierential equations become unbounded as the singular perturbation parameter " tends to zero. Therefore to approximate such derivatives, it is required to scale the derivatives in such a way that they are of order one for all values of the perturbation parameter. In practice , derivatives are related to the ux or drag and, hence, it is de...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2004
ISSN: 0377-0427
DOI: 10.1016/j.cam.2003.09.038