DiffMan User's Guide, Version 1.6

Kenth Engų, Arne Marthinsen and Hans Munthe-Kaas

Reports in Informatics No. 166, March 1999, Department of Informatics, University of Bergen, Norway.


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.