TY - JOUR
T1 - Splitting ADI Scheme for Fractional Laplacian Wave Equations
AU - Sun , Tao
AU - Sun , Hai-Wei
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 697
EP - 726
PY - 2024
DA - 2024/08
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2023-0149
UR - https://global-sci.org/intro/article_detail/nmtma/23371.html
KW - Operator splitting, alternative direction implicit scheme, Gohberg-Semencul formula, fractional Laplacian wave equation.
AB - <p style="text-align: justify;">In this paper, we investigate the numerical solution of the two-dimensional fractional Laplacian wave equations. After splitting out the Riesz fractional derivatives from the fractional Laplacian, we treat the Riesz fractional derivatives with an
implicit scheme while solving the rest part explicitly. Thanks to the tensor structure
of the Riesz fractional derivatives, a splitting alternative direction implicit (S-ADI)
scheme is proposed by incorporating an ADI remainder. Then the Gohberg-Semencul
formula, combined with fast Fourier transform, is proposed to solve the derived
Toeplitz linear systems at each time integration. Theoretically, we demonstrate that
the S-ADI scheme is unconditionally stable and possesses second-order accuracy.
Finally, numerical experiments are performed to demonstrate the accuracy and efficiency of the S-ADI scheme.</p>