DiffMan User's Guide, Version 1.6
Reports in Informatics No. 166, March 1999, Department of
Informatics, University of Bergen, Norway.
Preface
DiffMan is a MATLAB
toolbox for solving Ordinary Differential Equations on manifolds,
based on the concept of 'Coordinate Free Numerics'. This is, loosely
speaking, the idea that (whenever possible) it is important to
formulate numerical algorithms generically, independent of special
representations and coordinate systems. DiffMan inherits its basic
design philosophy from the C++ package SOPHUS. The SOPHUS project was
initiated by Magne Haveraaen and Hans Munthe-Kaas, University of
Bergen, and aims at solving tensor field equations on sequential and
parallel computers.
Some of the mathematical background of DiffMan is described in
Appendix A. This chapter, however, is included for the sake of
completeness. The user can read the rest of the manual and use DiffMan
without having studied this chapter.
The writing of this toolbox was initiated as a project within the
SYNODE project, and a number of papers describing the numerical
methods in DiffMan is available on the SYNODE home page at URL http://www.math.ntnu.no/num/synode/.
We will thank Antonella Zanna for reading an earlier version of this
User's Guide and always giving helpful suggestions, and Martine T.
Monsen for extensive proof reading.
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