2024/09/13 by Baolin Kuang, Hongfei Fu, Kuang, Baolin +3
Mathematics · #35K55 #65M06 #65M15 #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2409.08531
openalex publication_date 2024/09/13 · openalex created_date 2024/10/23 · openalex updated_date 2026/07/28
In this paper, we derive two bound-preserving and mass-conserving schemes based on the fractional-step method and high-order compact (HOC) finite difference method for nonlinear convection-dominated diffusion equations. We split the one-dimensional equation into three stages, and employ appropriate temporal and spatial discrete schemes respectively. We show that our scheme is weakly monotonic and that the bound-preserving property can be achieved using the bound-preserving limiter under some mild step constraints. By employing the alternating direction implicit (ADI) method, we extend the scheme to two-dimensional problems, further reducing computational cost. We also provide various numerical experiments to verify our theoretical results.