Fast numerical solution for fractional diffusion equations by exponential quadrature rule
| Autor: | Hai-Wei Sun, Hong-Kui Pang, Lu Zhang |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Discretization Applied Mathematics Mathematical analysis Gauss–Kronrod quadrature formula Tanh-sinh quadrature Computer Science Applications Arnoldi iteration Computational Mathematics symbols.namesake Matrix (mathematics) Modeling and Simulation symbols Gaussian quadrature Matrix exponential Coefficient matrix Mathematics |
| Zdroj: | Journal of Computational Physics. 299:130-143 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2015.07.001 |
| Popis: | After spatial discretization to the fractional diffusion equation by the shifted Grunwald 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. The matrix of the spatial discretization of the fractional diffusion equation is Toeplitz-like.An exponential quadrature rule is employed to solve the system of ordinary differential equations.The Toeplitz-like matrix exponential is calculated by the shift-invert Arnoldi method.The coefficient matrix satisfies a condition that guarantees the fast approximation by the shift-invert Arnoldi method.Numerical results show the efficiency of the exponential quadrature rule. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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