East Asian J. Appl. Math., 11 (2021), pp. 647-673.
Published online: 2021-08
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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.
}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.271220.090121}, url = {http://global-sci.org/intro/article_detail/eajam/19366.html} }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.