2016/07/23 by Bangti Jin, Buyang Li, Jin, Bangti +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1607.06948
openalex publication_date 2016/07/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work, we analyze a Crank-Nicolson type time stepping scheme for the subdiffusion equation, which involves a Caputo fractional derivative of order α∈ (0,1) in time. It hybridizes the backward Euler convolution quadrature with a θ-type method, with the parameter θ dependent on the fractional order α by θ=α/2, and naturally generalizes the classical Crank-Nicolson method. We develop essential initial corrections at the starting two steps for the Crank-Nicolson scheme, and together with the Galerkin finite element method in space, obtain a fully discrete scheme. The overall scheme is easy to implement, and robust with respect to data regularity. A complete error analysis of the fully discrete scheme is provided, and a second-order accuracy in time is established for both smooth and nonsmooth problem data. Extensive numerical experiments are provided to illustrate its accuracy, efficiency and robustness, and a comparative study also indicates its competitive with existing schemes.