Paper Info
Title
Grid Approximations of the Solution and Diffusion Flux for Singularity Perturbed Equations with Neumann Boundary Conditions
Abstract
Neumann problems for singularly perturbed parabolic equations are considered on a segment and on a rectangle. The second-order derivatives are multiplyed by a small parameter 2. When =0, the parabolic equation degenerates, and only the time derivative remains. The normalized diffusion flux, i.e., the product of and the derivative in the direction of normal, is given on the boundary. The solution of a classical discretization method on a uniform grid does not converge -uniformly. Moreover, we show with numerical examples that, in the case of a Neumann problem, the approximate solution and, thereupon, the discretization error may increase without bound for a vanishing . The error can exceed the real solution many times for small . For the solution of the boundary value problems new special finite difference schemes are constructed. These schemes allow us to approximate the solution and the normalized diffusion fluxes -uniformly.
Year
DOI
Venue
1996
10.1007/3-540-62598-4_123
WNAA
Keywords
Field
DocType
neumann boundary conditions,grid approximations,diffusion flux,singularity perturbed equations,neumann problem,singular perturbation,parabolic equation,boundary value problem,neumann boundary condition,second order
Boundary value problem,Robin boundary condition,Mathematical analysis,Free boundary problem,Poincaré–Steklov operator,Cauchy boundary condition,Neumann boundary condition,Von Neumann stability analysis,Mathematics,Mixed boundary condition
Conference
ISBN
Citations 
PageRank 
3-540-62598-4
0
0.34
References 
Authors
1
1
Name
Order
Citations
PageRank
Grigorii I. Shishkin15215.80