DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds

We describe an object-oriented MATLAB toolbox for solving differential equations on manifolds. The software reflects recent development within the area of geometric integration. Through the use of elements from differential geometry, in particular Lie groups and homogeneous spaces, coordinate free f...

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Veröffentlicht in:Applied numerical mathematics Jg. 39; H. 3; S. 323 - 347
Hauptverfasser: Engø, Kenth, Marthinsen, Arne, Munthe-Kaas, Hans Z.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2001
Schlagworte:
Free Lie algebras
Geometric integration
Homogeneous spaces
Lie algebras
Lie groups
MATLAB
Numerical analysis
Numerical integration of ordinary differential equations on manifolds
Object-oriented programming
Numerical integration of ordinary differential equations on manifolds
Numerical analysis
Homogeneous spaces
Lie algebras
Lie groups
Free Lie algebras
Object-oriented programming
MATLAB
Geometric integration
ISSN:0168-9274, 1873-5460
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Zusammenfassung:We describe an object-oriented MATLAB toolbox for solving differential equations on manifolds. The software reflects recent development within the area of geometric integration. Through the use of elements from differential geometry, in particular Lie groups and homogeneous spaces, coordinate free formulations of numerical integrators are developed. The strict mathematical definitions and results are well suited for implementation in an object-oriented language, and, due to its simplicity, the authors have chosen MATLAB as the working environment. The basic ideas of DiffMan are presented, along with particular examples that illustrate the working of and the theory behind the software package.
ISSN:0168-9274
1873-5460
DOI:10.1016/S0168-9274(00)00042-8