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On uniform difference schemes of a high order of approximation for evolution equations with a small parameter. (English) Zbl 0675.65055
The author considers initial value problems for the evolution equation ϵv ' +Av=f where ϵ is a small parameter and constructs difference schemes with a high order or approximation that are uniform in ϵ(0,1]. He points out that in order to implement his methods it is necessary to compute high order approximations to exp(-A h ) where A h is the discrete approximation to A.
Reviewer: J.P.D.Donnelly
MSC:
65J10Equations with linear operators (numerical methods)
65M06Finite difference methods (IVP of PDE)
65L05Initial value problems for ODE (numerical methods)
34G10Linear ODE in abstract spaces
34E15Asymptotic singular perturbations, general theory (ODE)
35B25Singular perturbations (PDE)
35G10Initial value problems for linear higher-order PDE
35K25Higher order parabolic equations, general