TY - JOUR
T1 - A Fast Temporal Second-Order Compact ADI Scheme for Time Fractional Mixed Diffusion-Wave Equations
AU - Du , Rui-Lian
AU - Sun , Zhi-Zhong
JO - East Asian Journal on Applied Mathematics
VL - 4
SP - 647
EP - 673
PY - 2021
DA - 2021/08
SN - 11
DO - http://doi.org/10.4208/eajam.271220.090121
UR - https://global-sci.org/intro/article_detail/eajam/19366.html
KW - Time fractional mixed diffusion-wave equations, SOEs technique, ADI difference scheme, stability, convergence.
AB - <p style="text-align: justify;">A fast temporal second-order compact alternating direction implicit (ADI) difference scheme is proposed and analysed for 2D time fractional mixed diffusion-wave
equations. The time fractional operators are approximated by mixed fast $L2$-$1_σ$ and
fast $L1$-type formulas derived by using the sum-of-exponentials technique. The spatial
derivatives are approximated by the fourth-order compact difference operator, which
can be implemented by an ADI approach with relatively low computational cost. The
resulting fast algorithm is computationally efficient in long-time simulations since the
computational cost is significantly reduced. Numerical experiments confirm the effectiveness of the algorithm and theoretical analysis.</p>