Prof. Dr. Kai Diethelm
AG Numerik
Institut Computational Mathematics
Technische Universität
Braunschweig
Pockelsstraße 14
38106 Braunschweig
Phone +49 531 391-7537 (secretary)
Fax +49 531 391-8206
e-mail:
K.Diethelm@tu-bs.de
Research interests
- Numerical integration (with an emphasis on singular and hypersingular
integrals)
- Integral equations and their numerical solution
- Approximation theory
- Fractional calculus; Fractional differential equations and their
numerical solution
- Finite elements (including aspects like mesh generation and the
implementation of FE methods on parallel computers using, e.g., the
FETI [Finite Element Tearing and Interconnecting] principle)
Publications
I am a member of the Editorial Board of the journals
and
,
and I work as a reviewer for
Software
Over the recent years, some of my co-workers and myself
have developed a number of software packages,
mostly in connection with numerical methods for fractional differential
equations (unless explicitly stated otherwise, the fractional derivatives
treated here must be interpreted in Caputo's sense).
Following a number of requests from various people,
I have decided to make them publicly available one after the other.
So far, you may download the following packages:
- The fractional Adams method
(Fortran 77 version)
This algorithm has been first introduced in the papers
[21] and
[23] of
my list of publications. More details are given in
[32], and a complete
theoretical analysis is contained in [36].
A synopsis and a comparison with other methods may be found in
[47]. The extensions indicated
in [33],
[34],
[35] and
[38] have not been included
into the implementation yet.
- The fractional backward differentiation formula (BDF)
(Fortran 77 version)
This is the algorithm described in
[12]. Notice that it differs from the fractional BDFs discussed
by Lubich in a series of papers in the 1980s. The implementation
provided here is somewhat restricted in that it can only handle
linear differential equations, i.e. equations of the form
Dq*y(t) = g(t) y(t) + f(t). Moreover it
only deals with the case 0 < q < 1. I plan to provide a version
without these restrictions when I find a little bit of time.
(in German)
Some useful links to the world of mathematics
Haftungsausschluss/
Disclaimer
K.Diethelm@tu-bs.de
,
and 
.