Electron. J. Diff. Equ.,
Vol. 2016 (2016), No. 118, pp. 1-14.
Convergence of iterative methods for elliptic equations with integral
boundary conditions
Mifodijus Sapagovas, Olga Stikoniene, Regimantas Ciupaila, Zivile Joksiene
Abstract:
In this article, we consider the convergence of iterative method for the
system of difference equations, approximating the elliptic two-dimensional
equations with variable coefficients and integral boundary conditions.
We investigate how convergence of iterative method depends on the structure
of spectrum for difference operator with nonlocal conditions.
The main goal of the paper is to analyze the influence of the monotonicity
of the coefficient in the differential equation to extension (or reduction)
of the region of convergence.
Submitted March 14, 2016. Published May 11, 2016.
Math Subject Classifications: 35J25, 65N06, 65N22, 35P15.
Key Words: Elliptic equation; finite-difference method; iterative method;
integral boundary conditions; eigenvalue problem; region of convergence.
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Mifodijus Sapagovas
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: mifodijus.sapagovas@mii.vu.lt
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Olga Stikoniene
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: olga.stikoniene@mif.vu.lt
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Regimantas Ciupaila
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: regimantas.ciupaila@vgtu.lt
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Zivile Joksiene
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: zivile.joksiene@fc.lsmuni.lt
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