Efficient Numerical Methods for Fractional Differential Equations
Afshin Farhadi (Technical University of Applied Sciences Würzburg-Schweinfurt, Faculty of Applied Natural Sciences and Humanities (FANG))
The approximate evaluation of fractional Riemann-Liouville integrals
in their traditional representation leads to complex computations that
require a relatively high memory and large amount of time when they are
implemented on a computer. In this talk, our aim is to introduce the
concept of a so-called diffusive representation (or infinite state
representations). This is an approach on which we can construct very
efficient numerical algorithms with respect to both the run time and the
memory issues for computing fractional integrals. Indeed such
representations can lead to numerical methods with small run time and
low memory requirements. We additionally show how one can apply such
diffusive-representation-based algorithms to solve fractional ordinary
differential equations in a fast and highly accurate way.
The work presented in this conference is related to a joint project with
Prof. Kai Diethelm and Dr. Renu Chaudhary (THWS) and Dr. André Schmidt
and Paul E. Haacker (Institute of Nonlinear Mechanics, Universität
Stuttgart). This project is supported by the German Federal Ministry of
Education and Research (BMBF) under Grant 05M22WHA.