2019/11/25 by Yayun Fu Wenjun Cai, Cai, Yayun Fu Wenjun, Yushun Wang +1
Computer Science · Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations #cs.NA #math.NA
paper · pdf · doi:10.48550/arxiv.1911.10845
26 pages, 13 figures
openalex publication_date 2019/11/25 · arxiv created 2019/11/26 · arxiv updated 2019/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper aims to construct structure-preserving numerical schemes for multi-dimensional space fractional Klein-Gordon-Schrödinger equation, which are based on the newly developed partitioned averaged vector field methods. First, we derive an equivalent equation, and reformulate the equation as a canonical Hamiltonian system by virtue of the variational derivative of the functional with fractional Laplacian. Then, we develop a semi-discrete conservative scheme via using the Fourier pseudo-spectral method to discrete the equation in space direction. Further applying the partitioned averaged vector field methods on the temporal direction gives a class of fully-discrete schemes that can preserve the mass and energy exactly. Numerical examples are provided to confirm our theoretical analysis results at last.