Numerical solutions of Bitsadze-Samarskii problem for elliptic equations.

*(English)* Zbl 1180.65104
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 (ISBN 978-981-283-732-5/hbk). 698-706 (2009).

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:

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) |