Abstract
The authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order p + r , where r = 2 and p is the order of the method. This generalization of conjugate-symplecticity states that the methods conserve quadratic first integrals and the Hamiltonian function over time intervals of length O ( h − r ) . Theorem 1 of the above mentioned paper is then replaced by a new one. All the other results in the paper do not change. Two new figures related to the already considered Kepler problem are also added.
Highlights
In paper [1] we analyzed the numerical solution of the first order Ordinary Differential
We considered the numerical solution of Hamiltonian problems which in canonical form can be written as follows: y 0 = J ∇ H ( y ), y(t0 ) = y0 ∈ IR2`, (3)
The class of Euler–Maclaurin Hermite–Obreshkov (EMHO) methods for the solution of Hamiltonian problems has been analyzed in [4] where the conjugate symplecticity up to order p + 2 of the p-th order methods was proven
Summary
We recall that a one-step numerical method Φh : IR2` → IR2` with stepsize h is symplectic if the discrete flow yn+1 = Φh (yn ), n ≥ 0, satisfies: Two numerical methods Φh , Ψh are conjugate to each other if there exists a global change of coordinates χh , such that: Ψh = χh ◦ Φh ◦ χ−
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