DiffMan
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 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.
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References in zbMATH (referenced in 10 articles , 1 standard article )
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Sorted by year (- Zadra, Michele; Mansfield, Elizabeth L.: Using Lie group integrators to solve two and higher dimensional variational problems with symmetry (2019)
- Bogfjellmo, Geir; Marthinsen, Håkon: High-order symplectic partitioned Lie group methods (2016)
- Celledoni, Elena; Iserles, Arieh; Nørsett, Syvert P.; Orel, Bojan: Complexity theory for Lie-group solvers (2002)
- Diele, F.; Politi, T.; Sgura, I.: A Fortran90 routine for the solution of orthogonal differential problems (2002)
- Saenz, Leonardo; Suarez, Rodolfo: A combinatorial approach to the generalized Baker-Campbell-Hausdorff-Dynkin formula (2002)
- Engø, Kenth; Marthinsen, Arne; Munthe-Kaas, Hans Z.: DiffMan: An object-oriented MATLAB toolbox for solving differential equations on manifolds (2001)
- Faltinsen, Stig; Marthinsen, Arne; Munthe-Kaas, Hans Z.: Multistep methods integrating ordinary differential equations on manifolds (2001)
- Iserles, A.; Nørsett, S. P.; Rasmussen, A. F.: Time symmetry and high-order Magnus methods (2001)
- Iserles, Arieh: How large is the exponential of a banded matrix? (2000)
- Iserles, Arieh: Lie groups and the computation of invariants (1999)