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  4. Numerical simulation by Deep Learning for discrete nonlinear problems involving the anisotropic p(.)-Laplacian

Numerical simulation by Deep Learning for discrete nonlinear problems involving the anisotropic p(.)-Laplacian

MMC.
2025;
Volume 12, Number 2
: pp. 549–557
https://doi.org/10.23939/mmc2025.02.549
Received: April 05, 2025
Revised: June 03, 2025
Accepted: June 05, 2025

Joubbi I., Aqel F., Sanou R., Alaa N. E.  Numerical simulation by Deep Learning for discrete nonlinear problems involving the anisotropic $\vec{p}(\cdot)$-Laplacian.  Mathematical Modeling and Computing. Vol. 12, No. 2, pp. 549–557 (2025)  

Authors:
  1. I. Joubbi
  2. F. Aqel
  3. R. Sanou
  4. N. E. Alaa
1
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University
2
Laboratory for Monitoring Emerging Technologies (LAVETE), Faculty of Sciences and Technics, Hassan First University
3
Laboratoire de Mathématiques et Informatique (LAMI), UFR Sciences Exactes et Appliquées, Université Thomas SANKARA
4
Laboratory LAMAI, Faculty of Science and Technology, Cadi Ayyad University

In this paper, we establish the existence of a class of discrete nonlinear systems involving the anisotropic $\vec{p}(\cdot)$-Laplacian operator using an optimization based approach.  We then simulate the solutions by implementing a deep learning model.  The numerical results demonstrate that the proposed method is stable and robust compared to conventional approaches such as the Newton–Krylov method.

discrete boundary value problem
deep learning
anisotropic p(.)-Laplacian
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