2018/12/18 by Kailai Xu, Xu, Kailai, Eric Darve +1
Mathematics · #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1812.08324
openalex publication_date 2018/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Modeling via fractional partial differential equations or a Lévy process has been an active area of research and has many applications. However, the lack of efficient numerical computation methods for general nonlocal operators impedes people from adopting such modeling tools. We proposed an efficient solver for the convection-diffusion equation whose operator is the infinitesimal generator of a Lévy process based on H-matrix technique. The proposed Crank Nicolson scheme is unconditionally stable and has a theoretical O(h2+Δt2) convergence rate. The H-matrix technique has theoretical O(N) space and computational complexity compared to O(N2) and O(N3) respectively for the direct method. Numerical experiments demonstrate the efficiency of the new algorithm.