4 problems

Symplecticity conjecture. The explicit method $\widetilde{\Phi}_h$ remains symplectic when the two weight vectors satisfy $\lambda=\xi$ and are freely selected.

Simulation conjecture. There exists a set

Let $\Phi_h$ be a basic symplectic partitioned Runge–Kutta (SPRK) method, and form a symmetric composition … where $\gamma_i=\gamma_{s+1-i}$ for $i=1,2,\ldots,\lfloor s/2\rfloor$.…

Let $s$ be the number of stages of a Lobatto IIIA–Lobatto IIIB method, and let $z$ denote the scaled frequency parameter for the elliptic test system. The elliptic structure-preser…