Open AccessHigh order compact difference scheme for solving the time multi-term fractional sub-diffusion equations
Author(s) -
Lei Ren
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022508
Subject(s) - mathematics , term (time) , convergence (economics) , stability (learning theory) , compact finite difference , order (exchange) , diffusion , finite difference method , scheme (mathematics) , differential equation , diffusion equation , mathematical analysis , finite difference , space (punctuation) , fractional calculus , computer science , physics , economy , finance , service (business) , quantum mechanics , machine learning , economics , economic growth , operating system , thermodynamics
In this paper, a high order compact finite difference is established for the time multi-term fractional sub-diffusion equation. The derived numerical differential formula can achieve second order accuracy in time and four order accuracy in space. A unconditionally stable and convergent difference scheme is presented, and a rigorous proof for the stability and convergence is given. Numerical results demonstrate the efficiency of the proposed difference schemes.