On the convergence to equilibria of a sequence defined by an implicit scheme

Thierry Horsin; Mohamed Ali Jendoubi

doi:10.3934/dcdss.2020465

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2021, Volume 14, Issue 8: 3017-3025. Doi: 10.3934/dcdss.2020465

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On the convergence to equilibria of a sequence defined by an implicit scheme

Thierry Horsin^1, , and
Mohamed Ali Jendoubi^2,3,

1.
Laboratoire M2N, EA7340, CNAM, 292 rue Saint-Martin, 75003, Paris, France
2.
Université de Carthage, Institut Préparatoire aux Etudes Scientifiques et Techniques, B.P. 51 2070 La Marsa, Tunisie
3.
Laboratoire équations aux dérivées partielles, Faculté des sciences de Tunis, Université Tunis El Manar, Campus universitaire El-Manar, 2092 El-Manar, Tunisie

^* Corresponding author: Thierry Horsin
^* Corresponding author: Thierry Horsin

Dedicated to the memory of Ezzeddine ZAHROUNI
Both authors wishes to thank Morgan Pierre for fruitful comments. They are also grateful to the referees for their very useful comments. The first author wishes to thanks the organizers of ICAAM 2019 in Hammamet, Tunisia, where this work was initiated. The second author wishes to thanks CNAM, France where this work was partially completed.

Received: August 31, 2020

Revised: September 30, 2020

Early access: November 2020

Published: August 2021

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Abstract

We present numerical implicit schemes based on a geometric approach of the study of the convergence of solutions of gradient-like systems given in [3]. Depending on the globality of the induced metric, we can prove the convergence of these algorithms.

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Mathematics Subject Classification: Primary: 34D05, 65L07; Secondary: 34C40.

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References

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