UM ETheses Collection (澳門大學電子學位論文庫)
 Title

A fast solution strategy for tempered fractional diffusion equations
 English Abstract

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An O(n log n) direct solution method, based on circulant and skewcirculant representation (CSR) for Toeplitz matrix inversion, where n is the total number of spatial grid points, is proposed for solving onedimensional (1D) and twodimensional (2D) tempered fractional diffusion equations with constant coefficients. It is proved that the CSR for the inverse of the coefficient matrix for 1D problems can be obtained in O(n log n) operations with circulant preconditioner. For 2D problems, where the total number of spatial grid points n = nxny, the operation cost to obtain the CSR is O(p log p), where p = max{nx, ny}, which is negligible in the whole process of solving the tempered fractional diffusion equation. Numerical experiments reveal that the proposed method is second order accurate and the computations are very efficient.
 Issue date

2016.
 Author

Fan, Dao Ying
 Faculty

Faculty of Science and Technology
 Department

Department of Mathematics
 Degree

M.Sc.
 Subject

Fractional calculus
Fractional differential equations
Differential equations  Numerical solutions
 Supervisor

Lei, Siu Long
 Files In This Item
 Location
 1/F Zone C
 Library URL
 991001944469706306