11 problems

Error comparison conjecture. Retraction-map-based integrators associated with retraction maps that are better approximations of the Riemannian exponential map on the configuration…

Hamiltonian-structure conjecture. The modifying vector field $\hat{f}_h$ is Hamiltonian at every order in its expansion in $h$.

Consider the stochastic Maxwell–Bloch system with $\sigma_1=\sigma_3=1$, the proposed explicit stochastic Poisson integrator, and a test function used to measure weak error. Weak c…

Consider the stochastic Maxwell–Bloch system and the proposed explicit stochastic Poisson integrator, with noise parameter $\sigma_1=0$. Strong convergence of order $1$ means that…

Consider the Yoshida technique applied to methods for highly oscillatory problems, using step sizes $alpha h$ and $beta h$ rather than a single step size $h$. Resonance conjecture.…

Consider standard finite element methods and their invariantised counterparts for ordinary differential equations, where invariantisation modifies a discretisation to preserve Lie…

Lie point symmetry-preserving schemes are numerical schemes for ordinary differential equations designed to preserve Lie point symmetries, while energy-preserving and symplectic me…

Euclidean freeness conjecture. The class of systems with Euclidean kinetic energy metrics is already free: the only linear identities satisfied by the Lie brackets of all such syst…

Nonexistence conjecture. Within the framework of csRK methods, there exists no computational energy-preserving method that is conjugate to a symplectic method.

Uniform-in-time invariant conservation conjecture. Symmetric UOSMs conserve invariants to

Piecewise-smooth numerical Hamiltonian gluing conjecture. A piecewise-smooth numerical Hamiltonian system for the full inequality constrained system can be constructed by gluing to…