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
Olga Stikoniene
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: olga.stikoniene@mif.vu.lt
Regimantas Ciupaila
Institute of Mathematics and Informatics
Vilnius University, Akademijos 4
LT-08663 Vilnius, Lithuania
email: regimantas.ciupaila@vgtu.lt
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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