Abstract: In this talk, I will present a non-polynomial spectral Petrov-Galerkin method and associated collocation method for substantial fractional differential equations (FDEs). A class of generalized Laguerre polynomials is extended to form our basis. By a proper scaling of trial basis and test basis, the Petrov-Galerkin method results in a diagonal and thus well-conditioned linear systems for both fractional advection equation and fractional diffusion equation. In the meantime, I will provide explicit forms of spectral collocation matrix for both types of equations. Moreover, the proposed method allows us to adjust a parameter in basis selection according to different given data to maximize the convergence rate.

About the Speaker: Can Huang is an assistant professor at Xiamen University. His Ph.D. is from Wayne State University, USA -- his advisor was Prof. Zhimin Zhang, now at CSRC. He was a visiting research associate at Michigan State University for two years. His research interests are spectral methods for fractional differential equations and the stochastic simulation of chemical reaction networks.

                  

Date&Time: Februry 4, 2015 (Friday), 10:30 - 11:30 a.m. 
Location: 606 Conference Room