7 problems

Let $\mathcal{P},\mathcal{Q}\subseteq\mathbb{R}^{d}$ be closed and convex, and let $F:\mathcal{P}\rightarrow\mathbb{R}$ and $G:\mathcal{Q}\rightarrow\mathbb{R}$ be $L$-smooth of or…

Let $m=n$ and let the payoff matrix be the identity matrix $A=I$, so that the skew-gradient flow is Hamiltonian. Let $H$ be a convex, differentiable energy function satisfying mild…

Implicitness conjecture. Every symmetric resonance-based scheme is necessarily implicit.

Let $M_{1,1}$ and $M_{2,2}$ denote the quantities associated with the primary and secondary parts of the additive Runge--Kutta method, and let the primary method have a specified o…

Let an approximation scheme yield a symmetric discrete Lagrangian, and let the corresponding discrete right and left Hamiltonians be obtained from it. Adjointness conjecture. The d…

The discussion concerns symplectic numerical methods for Hamiltonian partial differential equations, including splitting schemes and symplectic Runge–Kutta methods subject to a Cou…

FLAVOR error-growth conjecture. The observed linear growth of the error with the total simulation time is a consequence of FLAVOR being symplectic, and this linear growth holds onl…