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Open Access Research

On a difference scheme of the second order of accuracy for elliptic-parabolic equations

Okan Gercek1* and Allaberen Ashyralyev12

Author Affiliations

1 Department of Mathematics, Fatih University, Büyükçekmece, Istanbul, Turkey

2 Department of Mathematics, ITTU, Ashgabat, Turkmenistan

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Boundary Value Problems 2012, 2012:80  doi:10.1186/1687-2770-2012-80

Published: 27 July 2012

Abstract

The second order of accuracy difference scheme generated by Crank-Nicholson difference scheme for approximately solving multipoint nonlocal boundary value problem is considered. Well-posedness of this difference scheme in Hölder spaces is established. Furthermore, as applications, coercivity estimates in Hölder norms for approximate solutions of the multipoint nonlocal boundary value problems for mixed type equations are obtained. Moreover, the method is illustrated by numerical examples.

Keywords:
difference scheme; elliptic-parabolic equation; well-posedness