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Exponential Quadrature Rule for Fractional Diffusion Equations

孙海卫教授(澳门大学)
2015-05-13 10:00-11:00  闵行数学楼102报告厅
 
报告人简介:
孙海卫教授,澳门大学数学系。1996年香港中文大学应用数学专业博士毕业。2001至2004年期间分别在美国肯塔基州大学高性能计算实验室和亚拉巴马州大学化学工程系做博士后,2004年到澳门大学数学系工作,研究领域包括数值线性代数,偏微分方程数值解和金融计算等。

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.
   
 
 
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