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Zbl 0663.65056
Ashyralyev, Allaberen
On uniform difference schemes of a higher order of approximation for elliptical equations with a small parameter.
(English)
[J] Appl. Anal. 36, No.3-4, 211-220 (1990). ISSN 0003-6811; ISSN 1563-504X/e

In a Banach space E we consider the following boundary value problem for an elliptic equation: $\epsilon v''(t)=Av(t)+f(t)$ (0$\le t\le 1)$, $v(0)=v\sb 0$, $v(1)=v\sb 1$ with a small parameter $\epsilon$. For this problem we construct difference schemes of higher order of approximation which are uniform with respect to the small parameter $\epsilon$.
[A.Ashyralyev]
MSC 2000:
*65J10 Equations with linear operators (numerical methods)
65L10 Boundary value problems for ODE (numerical methods)
34G10 Linear ODE in abstract spaces
34E15 Asymptotic singular perturbations, general theory (ODE)

Keywords: Banach space; boundary value problem; elliptic equation; small parameter; difference schemes

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