Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6931069 | Journal of Computational Physics | 2015 | 24 Pages |
Abstract
After spatial discretization to the fractional diffusion equation by the shifted Grünwald formula, it leads to a system of ordinary differential equations, where the resulting coefficient matrix possesses the Toeplitz-like structure. An exponential quadrature rule is employed to solve such a system of ordinary differential equations. The convergence by the proposed method is theoretically studied. In practical computation, the product of a Toeplitz-like matrix exponential and a vector is calculated by the shift-invert Arnoldi method. Meanwhile, the coefficient matrix satisfies a condition that guarantees the fast approximation by the shift-invert Arnoldi method. Numerical results are given to demonstrate the efficiency of the proposed method.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Lu Zhang, Hai-Wei Sun, Hong-Kui Pang,