2024/04/24 by Thi Tam Dang, Dang, Thi Tam, Trung Hau Hoang +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2404.15947
openalex publication_date 2024/04/24 · openalex created_date 2024/04/26 · openalex updated_date 2026/07/28
Splitting methods are a widely used numerical scheme for solving convection-diffusion problems. However, they may lose stability in some situations, particularly when applied to convection-diffusion problems in the presence of an unbounded convective term. In this paper, we propose a new splitting method, called the "Adapted Lie splitting method", which successfully overcomes the observed instability in certain cases. Assuming that the unbounded coefficient belongs to a suitable Lorentz space, we show that the adapted Lie splitting converges to first-order under the analytic semigroup framework. Furthermore, we provide numerical experiments to illustrate our newly proposed splitting approach.