Open AccessAn Efficient Compact Difference Method for Temporal Fractional Subdiffusion Equations
Author(s) -
Lei Ren,
Lei Liu
Publication year - 2019
Publication title -
advances in mathematical physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.283
H-Index - 23
eISSN - 1687-9139
pISSN - 1687-9120
DOI - 10.1155/2019/3263589
Subject(s) - algorithm , convergence (economics) , stability (learning theory) , computer science , order (exchange) , mathematics , machine learning , finance , economics , economic growth
In this paper, a high-order compact finite difference method is proposed for a class of temporal fractional subdiffusion equation. A numerical scheme for the equation has been derived to obtain 2 - α in time and fourth-order in space. We improve the results by constructing a compact scheme of second-order in time while keeping fourth-order in space. Based on the L 2 -1 σapproximation formula and a fourth-order compact finite difference approximation, the stability of the constructed scheme and its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Applications using two model problems demonstrate the theoretical results.