A Note on Stability of Parabolic Difference Equations on Torus

被引：1

作者：

Ashyralyev, Allaberen ^{[1
,2
,3
]}

Hezenci, Fatih ^{[4
]}

Sozen, Yasar ^{[5
]}

机构：

[1] Bahcesehir Univ, Dept Math, Istanbul, Turkiye

[2] Peoples Friendship Univ Russia, RUDN Univ, Moscow, Russia

[3] Inst Math & Math Modeling, Alma Ata, Kazakhstan

[4] Duzce Univ, Fac Sci & Arts, Dept Math, Konuralp Campus Cent, TR-81620 Duzce, Turkiye

[5] Hacettepe Univ, Dept Math, Ankara, Turkiye

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 2023年 / 44卷 / 06期

关键词：

Difference equations on manifolds; difference schemes; self-adjoint positive definite operator; well-posedness;

D O I：

10.1080/01630563.2023.2183509

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present article investigates nonlocal boundary value problems for parabolic equations of reverse type on torus. The first order of accuracy difference scheme for the numerical solution of nonlocal boundary value problems for parabolic equations on circle T-1 and torus T-2 are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Holder norms are established. Furthermore, theoretical results are supported by numerical experiments.

引用

页码：490 / 509

页数：20

共 50 条

[41] A note on the second order of accuracy difference schemes for hyperbolic-parabolic equations in a Hilbert space
Ashyralyev, A
Yurtsever, HA
PROCEEDINGS OF DYNAMIC SYSTEMS AND APPLICATIONS, VOL 4, 2004, : 556 - 562
[42] A NOTE ON STOCHASTIC DIFFERENCE EQUATIONS
MILLER, KS
ANNALS OF MATHEMATICAL STATISTICS, 1968, 39 (01): : 270 - &
[43] NOTE ON LINEAR DIFFERENCE EQUATIONS
HARRIS, WA
SIBUYA, Y
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1964, 70 (01) : 123 - &
[44] The stability of difference schemes of second-order of accuracy for hyperbolic-parabolic equations
Ashyralyev, A.
Yurtsever, H. A.
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2006, 52 (3-4) : 259 - 268
[45] Stability of a finite-difference problem for a system of parabolic equations with nonstandard boundary conditions
Mazhorova, OS
Popov, YP
Sakharchuk, AS
DIFFERENTIAL EQUATIONS, 1997, 33 (07) : 950 - 958
[46] STABILITY AND CONVERGENCE OF DIFFERENCE APPROXIMATIONS TO PSEUDO-PARABOLIC PARTIAL-DIFFERENTIAL EQUATIONS
FORD, WH
TING, TW
MATHEMATICS OF COMPUTATION, 1973, 27 (124) : 737 - 743
[47] Stability of difference problems generated by infinite systems of quasilinear parabolic functional differential equations
Jaruszewska-Walczak, Danuta
BULLETIN OF THE BELGIAN MATHEMATICAL SOCIETY-SIMON STEVIN, 2011, 18 (03) : 517 - 536
[48] STABILITY OF DIFFERENCE EQUATIONS
BELLMAN, R
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1946, 52 (07) : 613 - 613
[49] Quasiperiodic Solutions of Differential-Difference Equations on a Torus
A. M. Samoilenko
E. P. Belan
Journal of Dynamics and Differential Equations, 2003, 15 (2-3) : 305 - 325
[50] A NOTE ON GLOBAL ASYMPTOTIC STABILITY OF NON-LINEAR DIFFERENCE-EQUATIONS
SZIDAROVSZKY, F
OKUGUCHI, K
ECONOMICS LETTERS, 1988, 26 (04) : 349 - 352

← 1 2 3 4 5 →