Efficient implementation of geometric integrators for separable Hamiltonian problems
Luigi Brugnano, Gianluca Frasca Caccia, Felice Iavernaro
TL;DR
This paper presents an efficient iterative implementation of Hamiltonian Boundary Value Methods (HBVMs) for separable Hamiltonian problems, focusing on energy conservation and computational efficiency.
Contribution
It introduces a triangular splitting-based iterative procedure to solve the discrete problems generated by HBVMs for separable Hamiltonian systems.
Findings
Reduced computational cost for energy-conserving methods
Effective iterative solver for separable Hamiltonian problems
Preservation of energy during numerical integration
Abstract
We here investigate the efficient implementation of the energy-conserving methods named Hamiltonian Boundary Value Methods (HBVMs) recently introduced for the numerical solution of Hamiltonian problems. In this note, we describe an iterative procedure, based on a triangular splitting, for solving the generated discrete problems, when the problem at hand is separable.
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