Numerical investigation of alternating-direction method for Poisson equation with weighted integral conditions

Olga Štikonienė; Mifodijus Sapagovas

doi:10.15388/LMR.2010.14665

Articles

Olga Štikonienė

Vilnius University

http://orcid.org/0000-0002-0302-3449

Mifodijus Sapagovas

Vilnius University

Published 2010-10-22

https://doi.org/10.15388/LMR.2010.14665

PDF

Keywords

elliptic equation
nonlocal integral conditions
finite-difference method
alternating direction method
convergence of iterative method

How to Cite

Štikonienė O. and Sapagovas M. (2010) “Numerical investigation of alternating-direction method for Poisson equation with weighted integral conditions”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 385-390. doi: 10.15388/LMR.2010.14665.

Abstract

The present paper deals with a generalization of the alternating-direction implicit
(ADI) method for a two dimensional Poisson equation in a rectangle domain with a
weighted integral boundary condition in one coordinate direction. We consider the alternating
direction method for a system of difference equations that approximates Poisson equation
with weighed integral boundary conditions with the fourth-order accuracy. Sufficient conditions
of stability for ADI method are investigated numerically. An analysis of results of
computational experiments is presented.

PDF

This work is licensed under a Creative Commons Attribution 4.0 International License.

Please read the Copyright Notice in Journal Policy.

Downloads

Article Views | PDF Downloads

Range Graph | Chart Graph

Most read articles by the same author(s)

Mifodijus Sapagovas, Regimantas Čiupaila, Kristina Jakubėlienė, Stasys Rutkauskas, A new eigenvalue problem for the difference operator with nonlocal conditions , Nonlinear Analysis: Modelling and Control: Vol 24 No 3 (2019)
Mifodijus Sapagovas, Viktorija Griškonienė, Olga Štikonienė, Application of M-matrices theory to numerical investigation of a nonlinear elliptic equation with an integral condition , Nonlinear Analysis: Modelling and Control: Vol 22 No 4 (2017)
Feliksas Ivanauskas, Valdas Laurinavičius, Mifodijus Sapagovas, Anatolij Neciporenko, Reaction–diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor , Nonlinear Analysis: Modelling and Control: Vol 22 No 2 (2017)
Olga Štikonienė, Mifodijus Sapagovas, Regimantas Čiupaila, On iterative methods for some elliptic equations with nonlocal conditions , Nonlinear Analysis: Modelling and Control: Vol 19 No 3 (2014)
Ugnė Jankauskaitė, Olga Štikonienė, Modelling immune system dynamics: the interaction of HIV and recombinant virus , Lietuvos matematikos rinkinys: Vol 56 (2015): Ser. A
Regimantas Čiupaila, Kristina Pupalaigė, Mifodijus Sapagovas, On the numerical solution for nonlinear elliptic equations with variable weight coefficients in an integral boundary conditions , Nonlinear Analysis: Modelling and Control: Vol 26 No 4 (2021)