题目：Fast approximate methods for the variable-order fractional advection-diffusion equation with a nonlinear source term
报告人：庞宏奎 副教授 （江苏师范大学）
时间：2020/10/29 （周四）17:00-18:00
地点：数学学院425会议室
摘要：In this talk, we consider the numerical solution of the variable-order(VO) fractional differential equations by the finite difference scheme. The resulting linear systems are dense without Toeplitz-like structure due to the variable-exponential kernel of VO operators. Observing the smooth property of the off-diagonal entries, we proposed an algorithm to approximate the dense coefficient matrices by exploiting the Lagrange interpolation with Chebyshev nodes. Theoretical analyses show that the approximate matrix can be constructed inO(kN) function evaluations and requires O(kN) storage, where k is the number of interpolation nodes. In addition, the approximate matrix-vector multiplication can be carried out in O(kNlogN) operations which promises us to solve the approximated systems quickly by the Krylov subspace method. Preconditioning technique is ulitized to accelerate the convergence. Furthermore, we also give the stability and error analysis of the new scheme. Numerical experiments are given to demonstrate the efficiency of the proposed method.
