2018/05/04 by Yosra Hafiene, Hafiene, Yosra, Fadini, Jalal +4
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1805.01754
openalex publication_date 2018/05/04 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
In this paper we study numerical approximations of the evolution problem for the nonlocal p-Laplacian operator with homogeneous Neumann boundary conditions on inhomogeneous random convergent graph sequences. More precisely, for networks on convergent inhomogeneous random graph sequences (generated first by deterministic and then random node sequences), we establish their continuum limits and provide rate of convergence of solutions for the discrete models to their continuum counterparts as the number of vertices grows. Our bounds reveals the role of the different parameters, and in particular that of p and the geometry/regularity of the data.