On iterative methods for some elliptic equations with nonlocal conditions
Articles
Olga Štikonienė
Vilnius University
http://orcid.org/0000-0002-0302-3449
Mifodijus Sapagovas
Vilnius University
Regimantas Čiupaila
Vilnius Gediminas Technical University, Lithuania
Published 2014-10-30
https://doi.org/10.15388/NA.2014.3.14
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Keywords

elliptic equation
nonlocal conditions
finite difference method
M-matrices
iterative methods

How to Cite

Štikonienė O., Sapagovas M. and Čiupaila R. (2014) “On iterative methods for some elliptic equations with nonlocal conditions”, Nonlinear Analysis: Modelling and Control, 19(3), pp. 517-535. doi: 10.15388/NA.2014.3.14.

Abstract

The iterative methods for the solution of the system of the difference equations derived from the elliptic equation with nonlocal conditions are considered. The case of the matrix of the difference equations system being the M-matrix is investigated. Main results for the convergence of the iterative methods are obtained considering the structure of the spectrum of the difference operators with nonlocal conditions. Furthermore, the case when the matrix of the system of difference equations has only positive eigenvalues was investigated. The survey of results on convergence of iterative methods for difference problem with nonlocal condition is also presented.

1The research was partially supported by the Research Council of Lithuania (grant No. MIP-051/2011).

2The research was partially supported by the Research Council of Lithuania (grant No. MIP-047/2014).

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