Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Inherently energy conserving time finite elements for classical mechanics
Journal of Computational Physics
Numerical Analysis in Modern Scientific Computing: An Introduction
Numerical Analysis in Modern Scientific Computing: An Introduction
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Energy conservation is an essential property of conservative mechanical systems that should be carried over to the numerical solution. Betsch and Steinmann proposed recently perturbed potentials to achieve energy conservation in the time integration of N-body problems by Galerkin methods. In the present paper this approach is generalised to Nyström methods for Hamiltonian systems. A detailed analysis shows that energy conservation by perturbed potential functions does not affect the feasibility and (high) order of convergence of Nyström methods. Symmetry and reversibility properties are left unchanged as well. The theoretical results are illustrated by numerical tests indicating clearly the benefits of energy conserving methods in long-term simulations.