In this talk, I shall consider time-dependent Maxwell equations in Cole-Cole dispersive media. The Cole-Cole model is the standard Maxwell equation coupled with a fractional time derivative term, which challenges the design and analysis of its numerical algorithm. By adopting the Matrix diagonalization method, the semidiscretisation of the model can be broken into a set of ordinary integro-differential equations (OIDE) with weakly singular kernel. Then, we propose an ansatz of solution for OIDEs. Using the ansatz, together with mapped numerical quadrature technique and well-conditioned matrix technique, we are able to produce an accurate approximation for OIDEs and thus, the original model as well.

Dr. Can Huang obtained his Ph.D in applied mathematics at Wayne State University in 2011 supervised by Prof. Zhimin Zhang. He is now an assistant professor of Xiamen University. His research focuses on numerical methods for fractional (partial) differential equations, integral equations, and stochastic differential equations.