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Zbl 0675.65055
Ashyralyev, Allaberen
On uniform difference schemes of a high order of approximation for evolution equations with a small parameter.
(English)
[J] Numer. Funct. Anal. Optimization 10, No.5, 593-606 (1989). ISSN 0163-0563; ISSN 1532-2467/e

The author considers initial value problems for the evolution equation $\epsilon v'+Av=f$ where $\epsilon$ is a small parameter and constructs difference schemes with a high order or approximation that are uniform in $\epsilon\in (0,1]$. He points out that in order to implement his methods it is necessary to compute high order approximations to $\exp (-A\sb h)$ where $A\sb h$ is the discrete approximation to A.
[J.P.D.Donnelly]
MSC 2000:
*65J10 Equations with linear operators (numerical methods)
65M06 Finite difference methods (IVP of PDE)
65L05 Initial value problems for ODE (numerical methods)
34G10 Linear ODE in abstract spaces
34E15 Asymptotic singular perturbations, general theory (ODE)
35B25 Singular perturbations (PDE)
35G10 Initial value problems for linear higher-order PDE
35K25 Higher order parabolic equations, general

Keywords: evolution equation; small parameter; difference schemes; high order approximations

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