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A note on the conditioning of upwind schemes on Shishkin meshes. (English) Zbl 0861.65066
The discretization of the singularly perturbed convection-diffusion boundary value problems is presented. For this discretization upwind schemes on a Shishkin mesh are used. The conditioning of these upwind finite difference schemes (UFDS) is investigated. In the numerical illustration the condition numbers of the discrete problems produced using the above UFDS for the 1D-convection-diffusion, 2D-convection-diffusion and 2D-reaction-diffusion are calculated.
Reviewer: T.E.Simos (Xanthi)

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
35K57 Reaction-diffusion equations
65L12 Finite difference and finite volume methods for ordinary differential equations
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65F35 Numerical computation of matrix norms, conditioning, scaling
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