Fourth Edition of the International Conference on Research in Applied Mathematics and Computer Science ICRAMCS 2022
 March 24-25-26, 2022
Online and Face-to-Face Conference

ICRAMCS, 4 (2022) | Proceedings ISSN: 2605-7700

Research Communication | Open Access
Volume 2022 | Communication ID 158
Convergence of a Finite Volume Scheme for a Parabolic System Applied to Image Processing
Jamal Attmani, Karami Fahd, Atlas Abdelghafour, Meskine Driss
Academic Editor: Youssef EL FOUTAYENI
Received
Accepted
Published
January 22, 2022
March 03, 2145
April 15, 2145

Abstract: We analyze a finite volume scheme for a nonlinear reaction–diffusion, which is a modified Perona–Malik nonlinear image selective smoothing equation. We establish the existence and uniqueness of solutions to the finite volume scheme, and we prove that it converges to a weak solution. The convergence proof is based on L₂ a-priori estimates and using Kolmogorov’s compactness theorem. The numerical simulations are done to verify the efficiency and effectiveness of the scheme.