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=== Geometric integrators for Hamiltonian Systems === | === Geometric integrators for Hamiltonian Systems === | ||
[http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration | [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration Geometric (AKA Symplectic) integrators] are useful for | ||
multi-dimensional classical mechanics problems and for molecular dynamics simulations. | multi-dimensional classical mechanics problems and for molecular dynamics simulations. | ||
The odepkg package has a number of solvers for ODE, DAE and DDE problems but none of them is currently | The odepkg package has a number of solvers for ODE, DAE and DDE problems but none of them is currently | ||
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that of other functions in odepkg (or that of DASPK and LSODE) but will need specific extensions to accommodate for specific options that only make sense for this specific class of solvers. | that of other functions in odepkg (or that of DASPK and LSODE) but will need specific extensions to accommodate for specific options that only make sense for this specific class of solvers. | ||
An initial list of methods to be implemented includes (but is not limited to) | An initial list of methods to be implemented includes (but is not limited to) | ||
* Symplectic Euler methods, see [http://en.wikipedia.org/wiki/Semi-implicit_Euler_method here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration | * Symplectic Euler methods, see [http://en.wikipedia.org/wiki/Semi-implicit_Euler_method here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration here] | ||
* Störmer-Verlet method, see [http://en.wikipedia.org/wiki/Verlet_integration here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration | * Störmer-Verlet method, see [http://en.wikipedia.org/wiki/Verlet_integration here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration here] | ||
* Velocity Verlet method, see [http://en.wikipedia.org/wiki/Verlet_integration here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration | * Velocity Verlet method, see [http://en.wikipedia.org/wiki/Verlet_integration here] and [http://openlibrary.org/books/OL9056139M/Geometric_Numerical_Integration here] | ||
* Symplectic partitioned Runge-Kutta methods, see [http://reference.wolfram.com/mathematica/tutorial/NDSolveSPRK.html here] or [http://dx.doi.org/10.1137/0733019 here] | * Symplectic partitioned Runge-Kutta methods, see [http://reference.wolfram.com/mathematica/tutorial/NDSolveSPRK.html here] or [http://dx.doi.org/10.1137/0733019 here] | ||
* Spectral Variational Integrator methods, see [http://www3.nd.edu/~izaguirr/papers/acta_numerica.pdf here] or [http://www.math.ucsd.edu/~mleok/pdf/HaLe2012_SVI.pdf here] | * Spectral Variational Integrator methods, see [http://www3.nd.edu/~izaguirr/papers/acta_numerica.pdf here] or [http://www.math.ucsd.edu/~mleok/pdf/HaLe2012_SVI.pdf here] | ||