| Title |
On stability and convergence of difference schemes for one class of parabolic equations with nonlocal condition / |
| Authors |
Sapagovas, Mifodijus ; Novickij, Jurij ; Pupalaigė, Kristina |
| DOI |
10.15388/namc.2025.30.38346 |
| Full Text |
|
| Is Part of |
Nonlinear analysis: modelling and control.. Vilnius : Vilnius University Press. 2025, vol. 30, no. 1, p. 135-155.. ISSN 1392-5113. eISSN 2335-8963 |
| Keywords [eng] |
nonlocal boundary conditions ; finite-difference method ; stability and convergence ; majorant, M-matrices |
| Abstract [eng] |
In this paper, we construct and analyze the finite-difference method for a two-dimensional nonlinear parabolic equation with nonlocal boundary condition. The main objective of this paper is to investigate the stability and convergence of the difference scheme in the maximum norm. We provide some approaches for estimating the error of the solution. In our approach, the assumption of the validity of the maximum principle is not required. The assumption is changed to a weaker one: the difference problem’s matrix is the M-matrix. We present numerical experiments to illustrate and supplement theoretical results. |
| Published |
Vilnius : Vilnius University Press |
| Type |
Journal article |
| Language |
English |
| Publication date |
2025 |
| CC license |
|
