6 problems

Let $u^n$ be the numerical solution produced by the nonuniform-time-step GBDF2-IMEX scheme … Here $\tau=\max_{0\leq k\leq M-1}\{\Delta t_k\}$ is the maximum time step, and $h_x$ an…

Consider the gradient descent scheme with convex–concave splitting for the Allen–Cahn equation, and its energy-dissipation estimate, which includes the energy decrease and a neglec…

HOLO non-injectivity conjecture. The observed lack of consistency of HOLO is caused by $Delta t$ becoming sufficiently large that $\mathcal{E}^*$ is no longer injective.

Let $s$ be the order of the SAT time discretization, and interpret an $\eta$-CFL condition as a time-step constraint of the form … where $C$ is fixed, $\Delta t$ is the time-step s…

Taylor time-stepping methods have local stability radii that do not yield an order-independent CFL number. Stability-enhanced Taylor-scheme conjecture. Stability-enhanced schemes c…

Let $u$ be a sufficiently regular exact solution of the nonlinear Schrödinger equation, let $t_{n+\frac12}:=(t_{n+1}+t_n)/2$, and let $\Phi^{-\frac12}=|u_0|^{2p}$. For variable tim…