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Zbl 1180.65104
Ashyralyev, A.; Öztürk, E.
Numerical solutions of Bitsadze-Samarskii problem for elliptic equations. (English)
[A] Begehr, H. G. W. (ed.) et al., Further progress in analysis. Proceedings of the 6th international ISAAC congress, Ankara, Turkey, August 13--18, 2007. Hackensack, NJ: World Scientific. 698-706 (2009). ISBN 978-981-283-732-5/hbk

Summary: A numerical method is proposed for solving a Bitsadze-Samarskii-type nonlocal boundary value problem for multidimensional elliptic partial differential equations. Second and fourth orders of accuracy stable difference schemes are presented. The stability and almost coercive stability of these difference schemes are established. The method is illustrated by numerical examples.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35L20 Second order hyperbolic equations, boundary value problems
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: stability; numerical examples; Bitsadze-Samarskii problem; elliptic equation; nonlocal boundary value problems; difference scheme; linear second-order hyperbolic equation

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