In this paper we define an efficient implementation for the family of low-rank energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), recently defined in the last years. The proposed implementation relies on the particular structure of the Butcher matrix defining such methods, for which we can derive an efficient splitting procedure. The very same procedure turns out to be automatically suited for the efficient implementation of Gauss-Legendre collocation methods, since these methods are a special instance of HBVMs. The linear convergence analysis of the splitting procedure exhibits excellent properties, which are confirmed by a few numerical tests. © 2014 Springer Science+Business Media New York.
Efficient implementation of Gauss collocation and Hamiltonian boundary value methods
IAVERNARO, Felice
2014-01-01
Abstract
In this paper we define an efficient implementation for the family of low-rank energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs), recently defined in the last years. The proposed implementation relies on the particular structure of the Butcher matrix defining such methods, for which we can derive an efficient splitting procedure. The very same procedure turns out to be automatically suited for the efficient implementation of Gauss-Legendre collocation methods, since these methods are a special instance of HBVMs. The linear convergence analysis of the splitting procedure exhibits excellent properties, which are confirmed by a few numerical tests. © 2014 Springer Science+Business Media New York.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
