Chebyshev iteration for the problem with nonlocal boundary condition

Mifodijus Sapagovas; Artūras Štikonas; Olga Štikonienė

doi:10.15388/LMR.2004.15313

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Mifodijus Sapagovas

Vilnius University

Artūras Štikonas

Vilnius University

https://orcid.org/0000-0002-5872-5501

Olga Štikonienė

Vilnius University

Published 2004-12-17

https://doi.org/10.15388/LMR.2004.15313

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Keywords

Poisson differential equation
nonlocal boundary condition
ﬁnite difference scheme
Chebyshev iteration

How to Cite

Sapagovas, M., Štikonas, A. and Štikonienė, O. (2004) “Chebyshev iteration for the problem with nonlocal boundary condition”, Lietuvos matematikos rinkinys, 44(spec.), pp. 665–669. doi:10.15388/LMR.2004.15313.

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Abstract

We considered Poisson differential equation with Dirichlet boundary conditions and one nonlocal boundary condition. Finite-difference scheme was investigated for this problem. The eigenvalues of such problem depend on few parameters in the nonlocal boundary condition. The convergence rate for Cheby-shev iterations depends on the number of the discrete mesh points. The convergence is more faster when the maximal eigenvalue of the corresponding nonsimmetric matrix is simple.

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