Abstract
This paper proposes and analyzes a tempered fractional integrodifferential equation in three-dimensional (3D) space. The Crank-Nicolson (CN) method and trapezoidal convolution quadrature rule are used to approximate the time derivative and tempered fractional integral term respectively, and finite difference/compact difference approaches combined with corresponding alternating direction implicit (ADI) algorithms are employed for spatial discretizations, which obtains the fully discrete CN ADI finite difference/compact difference schemes. Then, convergence analysis of two kinds of ADI schemes is derived via the energy argument and the generating function of Toeplitz matrices. Provided numerical examples confirm our theoretical estimates.
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This work was supported by the National Natural Science Foundation of China (Nos. 12101080, 12126308, 12126303, 12071127).
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Qiao, L., Qiu, W. & Xu, D. Crank-Nicolson ADI finite difference/compact difference schemes for the 3D tempered integrodifferential equation associated with Brownian motion. Numer Algor 93, 1083–1104 (2023). https://doi.org/10.1007/s11075-022-01454-0
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DOI: https://doi.org/10.1007/s11075-022-01454-0