2020/06/19 by Muhammad Munir Butt, Butt, Muhammad Munir
Computer Science · Engineering · Mathematics · Physics and Astronomy · #35Q84 #49K20 #65N55 #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Theoretical and Computational Physics #cs.NA #math.NA #msc:35Q84 #msc:49K20 #msc:65N55
paper · pdf · doi:10.48550/arxiv.2006.11038
openalex publication_date 2020/06/19 · arxiv created 2020/06/26 · arxiv updated 2020/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A numerical solution to the Fokker-Planck equation using a two-level scheme is presented. The Fokker-Planck (FP) equation is of parabolic type equation govern the time evolution of probability density function of the stochastic processes. The FP equation also preserves the positivity and conservative of the total probability. A Chang-Cooper discretization scheme is used to ensure the positiveness and conservation of the total probability with second-order accuracy. We investigate a two-level scheme with factor-three-coarsening strategy and have a significant reduction in computations and CPU time. Numerical experiments are performed to validate the efficiency and second-order accuracy of the proposed two-level algorithm with backward time-difference schemes.