An α-robust fast algorithm for distributed-order time–space fractional diffusion equation with weakly singular solution
A fast algorithm is proposed for solving two-dimensional distributed-order time–space fractional diffusion equation where the solution has a weak singularity at initial time. The distributed-order fractional problem is firstly transformed into multi-term fractional problem by the Gauss–Legendre quad...
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| Vydané v: | Mathematics and computers in simulation Ročník 207; s. 437 - 452 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier B.V
01.05.2023
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| Predmet: | |
| ISSN: | 0378-4754, 1872-7166 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | A fast algorithm is proposed for solving two-dimensional distributed-order time–space fractional diffusion equation where the solution has a weak singularity at initial time. The distributed-order fractional problem is firstly transformed into multi-term fractional problem by the Gauss–Legendre quadrature formula. Then the exponential-sum-approximation method on graded mesh is utilized to discretize time Caputo fractional derivatives in time direction, and a standard finite difference method is employed to approximate the spatial Riesz fractional derivatives. The scheme is proved to be α-robust convergent analytically. The discrete linear system possesses symmetric positive definite block-Toeplitz–Toeplitz-block structure and is efficiently solved by conjugate gradient method with the state-of-the-art sine-transformed based preconditioner. Numerical examples confirm the error analysis and the effectiveness of the preconditioner. |
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| ISSN: | 0378-4754 1872-7166 |
| DOI: | 10.1016/j.matcom.2023.01.011 |