Energy conservation with non-symplectic methods:
examples and counter-examples
Erwan Faou, Ernst Hairer and Truong-Linh Pham
Abstract.
Energy conservation of numerical integrators is well understood
for symplectic one-step methods. This article provides new insight
into energy conservation with non-symplectic methods. Sufficient
conditions and counter-examples are presented.
Key Words.
Hamiltonian systems, energy conservation, backward error analysis,
symmetric and symplectic methods.