A Note on Stability of Parabolic Difference Equations on Torus

Ashyralyev A. Hezenci F. Sozen Y.
2023 Taylor and Francis Ltd.

Numerical Functional Analysis and Optimization
2023 #44 Issue 6 490 - 509 pp.

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 (Formula presented.) and torus (Formula presented.) are presented. For the solutions of the difference scheme, the stability estimates and coercivity estimates in various Hölder norms are established. Furthermore, theoretical results are supported by numerical experiments.

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

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Department of Mathematics, Bahcesehir University, Istanbul, Turkey
Peoples’ Friendship, University of Russia (RUDN University), Moscow, Russian Federation
Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
Department of Mathematics, Hacettepe University, Ankara, Turkey

Department of Mathematics
Peoples’ Friendship
Institute of Mathematics and Mathematical Modeling
Department of Mathematics
Department of Mathematics

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