A Hybrid Difference Scheme for a Second-Order Singularly Perturbed Reaction-Diffusion Problem with Non-smooth Data
نویسندگان
چکیده
منابع مشابه
A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction-diffusion problems
This paper deals with the numerical approximation of the solution of 1D parabolic singularly perturbed problems of reaction–diffusion type. The numerical method combines the standard implicit Euler method on a uniform mesh to discretize in time and a HODIE compact fourth order finite difference scheme to discretize in space, which is defined on a priori special meshes condensing the grid points...
متن کاملA second-order overlapping Schwarz method for a 2D singularly perturbed semilinear reaction-diffusion problem
An overlapping Schwarz domain decomposition is applied to a semilinear reaction-diffusion equation posed in a smooth two-dimensional domain. The problem may exhibit multiple solutions; its diffusion parameter ε2 is arbitrarily small, which induces boundary layers. The Schwarz method invokes a boundary-layer subdomain and an interior subdomain, the narrow subdomain overlap being of width O(ε| ln...
متن کاملA 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 کاملOn Stability of Spline Difference Scheme for Reaction–diffusion Time–dependent Singularly Perturbed Problem
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...
متن کاملSecond-order Numerical Scheme for Singularly Perturbed Reaction–Diffusion Robin Problems
In this article, we consider singularly perturbed reaction-diffusion Robin boundary-value problems. To solve these problems we construct a numerical method which involves both the cubic spline and classical finite difference schemes. The proposed scheme is applied on a piece-wise uniform Shishkin mesh. Truncation error is obtained, and the stability of the method is analyzed. Also, parameter-un...
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: International Journal of Applied and Computational Mathematics
سال: 2014
ISSN: 2349-5103,2199-5796
DOI: 10.1007/s40819-014-0004-8