Kernel-based Approximation Methods for Cauchy Problems of Fractional Order Partial Differential Equations
Speaker:Prof. Benny Hon
Department of Mathematics
City University of Hong Kong
Date & Time:3 Jun 2011 (Friday) 15:00 - 16:00
Venue:JM17
Organized by:Department of Mathematics

Abstract

In this talk we present the recent development of meshless computational methods based on the use of kernel-based functions for solving various inverse and ill-posed problems. Properties of some special kernels such as harmonic kernels; kernels from the construction of fundamental and particular solutions; Green's functions; and radial basis functions will be discussed. As an illustration, the recent work in using the method of fundamental solutions combined with the Laplace transform and the Tikhonov regularization techniques to solve Cauchy problems of Fractional Order Partial Differential Equations (FOPDEs) will be demonstrated. The main idea is to approximate the unknown solution by a linear combination of fundamental solutions whose singularities are located outside the solution domain. The Laplace transform technique is used to obtain a more accurate numerical approximation of the fundamental solutions and the L-curve method is adopted for searching an optimal regularization parameter in obtaining stable solution from measured data with noises.

Biography

Professor Hon received his Ph.D. in Applied Mathematics from the University of Louisiana at Lafayette, USA. He is presently the Professor of the Department of Mathematics, City University of Hong Kong, Hong Kong. He is now serving as the editor for six research journals and member on the Advisory Board for Gifted Education. His research interests include meshless computational methods, inverse problems, symbolic computation and gifted education. He has published over 120 research articles in the academic journals.