High-order Symmetric Schemes for the Energy Conservation of Polynomial Hamiltonian Problems

F. Iavernaro3
Dipartimento di Matematica, Universita di Bari, I-70125 Bari, Italy
D. Trigiante
Dipartimento di Energetica, Universita di Firenze, I-50134 Firenze, Italy
Received 11 March, 2009; accepted in revised form 23 April, 2009

Dedicated to John Butcher on the occasion of his 75th birthday
Abstract: We define a class of arbitrary high order symmetric one-step methods that, when applied to Hamiltonian systems, are capable of precisely conserving the Hamiltonian function when this is a polynomial, whatever the initial condition and the stepsize h used.
The key idea to devise such methods is the use of the so called discrete line integral, the discrete counterpart of the line integral in conservative vector fields. This approach naturally suggests a formulation of such methods in terms of block Boundary Value Methods, although they can be recast as Runge-Kutta methods, if preferred.

 

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