On the numerical solution for nonlinear elliptic equations with variable weight coefficients in an integral boundary conditions
Articles
Regimantas Čiupaila
Vilnius Gediminas Technical University
https://orcid.org/0000-0002-7910-3285
Kristina Pupalaigė
Kaunas University of Technology
https://orcid.org/0000-0001-6443-1756
Mifodijus Sapagovas
Vilnius University
https://orcid.org/0000-0002-7139-3468
Published 2021-07-01
https://doi.org/10.15388/namc.2021.26.23929
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Keywords

elliptic equation
nonlocal conditions
finite difference method
M-matrices
eigenvalue problem for difference operator
iterative methods

How to Cite

Čiupaila R., Pupalaigė K. and Sapagovas M. (2021) “On the numerical solution for nonlinear elliptic equations with variable weight coefficients in an integral boundary conditions”, Nonlinear Analysis: Modelling and Control, 26(4), pp. 738-758. doi: 10.15388/namc.2021.26.23929.

Abstract

In the paper the two-dimensional elliptic equation with integral boundary conditions is solved by finite difference method. The main aim of the paper is to investigate the conditions for the convergence of the iterative methods for the solution of system of nonlinear difference equations. With this purpose, we investigated the structure of the spectrum of the difference eigenvalue problem. Some sufficient conditions are proposed such that the real parts of all eigenvalues of the corresponding difference eigenvalue problem are positive. The proof of convergence of iterative method is based on the properties of the M-matrices not requiring the symmetry or diagonal dominance of the matrices. The theoretical statements are supported by the results of the numerical experiment.

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