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Palindromic 3 stage splitting integrators, a roadmap

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Figure

Figure 1: The (a, b) plane. Points on the discontinuous curve yield methods with enhanced conservation of energy for quadratic Hamiltonians.
Figure 2: The figure shows, for a ≥ b, the different possible cases that arise in the solution of the equations A h (z) = ±1 (see the text)
Figure 3: Possible behaviors of the polynomial A h (z). In panel number (9), the sequence 1, 1, 1, -1 indicates that as z increases, there is first an intersection with the line A h = 1, then a second intersection with A h = 1, then the intersection with A
Figure 4: (a, b) plane near Strang’s method. The dash/dot line corresponds to methods with high-order conservation of energy in the quadratic case.
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