Fast numerical solution for fractional diffusion equations by exponential quadrature rule ?
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.
fractional diffusion equation exponential quadrature rule matrix exponential shift-invert arnoldi toeplitz-like structure preconditioned gmres