CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM

Hajri Imen; Fethi Ben Belgacem

doi:10.11948/20230104

2024 Volume 14 Issue 1

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Hajri Imen, Fethi Ben Belgacem. CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 146-161. doi: 10.11948/20230104

Citation:

Hajri Imen, Fethi Ben Belgacem. CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 146-161. doi: 10.11948/20230104

CONVERGENT APPROACHES FOR THE DIRICHLET MONGE-AMPÈRE PROBLEM

Hajri Imen^1, ,,
Fethi Ben Belgacem^2,

1.
Department of Textile and Fashion Management, University of Monastir, Cornich 5000, Tunisia
2.
Laboratory of partial differential equations (LR03ES04), ISIMM, University of Monastir, Cornich 5000, Tunisia

Author Bio: Email: fethi.benbelgacem@isimm.rnu.tn(F. B. Belgacem)
Corresponding author: Email: hajri.imene2017@gmail.com(I. Hajri)

Abstract

Abstract

In this article, we introduce and study three numerical methods for the Dirichlet Monge-Ampère equation in two dimensions. The approaches consist in considering new equivalent problems. In the first method (method A) the equivalent problem is discretized by a wide stencil finite difference discretization and monotone schemes are obtained. Hence, we apply the Barles-Souganidis theory to prove the convergence of the schemes and the Damped Newtons method is used to compute the solutions of the schemes. In the last two methods (B and C) we introduce two fixed point operators. Finally, some numerical results are illustrated.
- Monge-Ampère /
- fixed point /
- wide stencil /
- Newton method
MSC: 35J99, 65N06

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References

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