期刊
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
卷 62, 期 1-2, 页码 449-472出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s12190-019-01291-w
关键词
Riesz fractional reaction-diffusion equation; Toeplitz structure; Exponential Runge-Kutta method; Matrix exponential; Shift-invert Lanczos method
A spatial discretization of the Riesz fractional nonlinear reaction-diffusion equation by the fractional centered difference scheme leads to a system of ordinary differential equations, in which the resulting coefficient matrix possesses the symmetric block Toeplitz structure. An exponential Runge-Kutta method is employed to solve such a system of ordinary differential equations. In the practical implementation, the product of a block Toeplitz matrix exponential and a vector is calculated by the shift-invert Lanczos method. Meanwhile, the symmetric positive definiteness of the coefficient matrix guarantees the fast approximation by the shift-invert Lanczos method. Numerical results are given to demonstrate the efficiency of the proposed method.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据