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Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution
sunlinan *,wangantao #
School of Mathematics and Statitics, Lanzhou University
*Correspondence author
#Submitted by
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Funding: none
Opened online:15 December 2008
Accepted by: none
Citation: sunlinan,wangantao.Uniform convergence analysis of an upwind finite difference approximations of an homogenous singularly perturbed boundary value problem using grid equidistribution[OL]. [15 December 2008] http://en.paper.edu.cn/en_releasepaper/content/26584
 
 
We derive varepsilon-uniform error estimates for two first-order upwind discretizations of a model inhomogeneous, second-order, singularly perturbed boundary value problem on a non-uniform grid. Here, varepsilon is the small parameter multiplying the highest derivative term. The grid is suggested by the equidistribution of a positive monitor function which is a linear combination of a constant floor and a power of the second derivative of the solution. Our analysis shows how the floor should be chosen to ensure varepsilon-uniform convergence and indicates the convergence behaviour for such grids.
Keywords:singular perturbation;adaptive grid;rate of convergence;error estimate
 
 
 

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