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Exponential Quadrature Rule for Fractional Diffusion Equations
孙海卫 教授(澳门大学 )
2018-01-01 12:13  华东师范大学

摘要:In this talk, we study the fractional diffusion equations. 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. This is a joint work with Lu Zhang and Hong-kui Pang.

主持人:潘建瑜 副教授