Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The Midpoint Scheme and Variants for Hamiltonian Systems: Advantages and Pitfalls
SIAM Journal on Scientific Computing
Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
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This paper studies conservative formulations for the evolution of flows in 3-D which satisfy a symmetry condition. It is shown how the Hamiltonian form leads to a proper form of the evolution equation. This is illustrated by a number of examples. It is also shown how this results in conservation of e.g. mass when using simplectic integrators. A special section is devoted to computing displacements by the implicit midpoint rule when the velocities are not available in explicit form but e.g. found from a numerical method like FEM.