TY - JOUR
T1 - Efficient and Stable Numerical Methods for Multi-Term Time Fractional Sub-Diffusion Equations
AU - Ren , Jincheng
AU - Sun , Zhi-Zhong
JO - East Asian Journal on Applied Mathematics
VL - 3
SP - 242
EP - 266
PY - 2018
DA - 2018/02
SN - 4
DO - http://doi.org/10.4208/eajam.181113.280514a
UR - https://global-sci.org/intro/article_detail/eajam/10835.html
KW - Multi-term time fractional sub-diffusion equations, compact/compact ADI difference scheme, discrete energy method, convergence.
AB - <p style="text-align: justify;">Some efficient numerical schemes are proposed for solving one-dimensional
(1D) and two-dimensional (2D) multi-term time fractional sub-diffusion equations, combining the compact difference approach for the spatial discretisation and $L1$ approximation for the multi-term time Caputo fractional derivatives. The stability and convergence of these difference schemes are theoretically established. Several numerical examples are implemented, testifying to their efficiency and confirming their convergence order.</p>