Overlapping Domain Decomposition Methods for Noncoercive Hamilton-Jacobi-Bellman Equation

Authors

  • Samar Chebbah Laboratoire des Mathématiques Appliquées et Didactique (MAD), École Normale Supérieure El Katiba Assia Djebar  (ENSC) – Constantine, Constantine, Algeria https://orcid.org/0009-0007-4147-990X
  • Mohamed Haiour Department of Mathematics, Faculty of the Sciences, University Badji Mokhtar, P.O 23000 Annaba, Algeria
  • Sofiane Madi Department of Mathematics, Faculty of Mathematics and Computer Science, University of Batna 2, Batna, Algeria

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.6070

Keywords:

Hamilton-Jacobi-Bellman equation, noncoercive problems, overlapping domain decomposition, convergence analysis, lower and upper solutions, finite difference method

Abstract

This study presents an approach to demonstrate the monotonic and geometric convergence of the non-coercive Hamilton-Jacobi-Bellman problem with Dirichlet boundary conditions using the finite difference method. The approach combines overlapping domain decomposition with a sequence of lower and upper solutions to characterize the solution in a discrete setting. Numerical experiments are conducted to validate the methodology and illustrate the consistency of the theoretical findings.

Author Biography

  • Samar Chebbah , Laboratoire des Mathématiques Appliquées et Didactique (MAD), École Normale Supérieure El Katiba Assia Djebar  (ENSC) – Constantine, Constantine, Algeria

    Department of Mathematics, Institute of Mathematics and Computer Science, Applied Mathematics and Didactics Laboratory, Ecole Normale Supérieure El Katiba Assia Djebar (ENSC) - Constantine,  Abdelhafid Boussouf University Center - Mila, Algeria.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Mathematical Modeling and Numerical Analysis

License

Copyright (c) 2025 Samar Chebbah , Mohamed Haiour, Sofiane Madi

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How to Cite

Overlapping Domain Decomposition Methods for Noncoercive Hamilton-Jacobi-Bellman Equation. (2025). European Journal of Pure and Applied Mathematics, 18(2), 6070. https://doi.org/10.29020/nybg.ejpam.v18i2.6070