We show that Kahan's discretization of quadratic vector fields is equivalent to a Runge–Kutta
method. When the vector field is Hamiltonian on either a symplectic vector space or a …

It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, ie, the
free-energy functional decreases in time. Linearly implicit integrators have been developed …

One of the most demanding calculations is to generate random samples from a specified
probability distribution (usually with an unknown normalizing prefactor) in a high …

We give an overview of the integrability of the Hirota-Kimura discretizationmethod applied to
algebraically completely integrable (aci) systems with quadratic vector fields. Along with the …

Leapfrog integration has been the method of choice in N-body simulations owing to its low
computational cost for a symplectic integrator with second order accuracy. We introduce a …

There has been considerable recent work on the development of energy conserving one-
step methods that are not symplectic. Here we extend these ideas to stochastic Hamiltonian …

We present several novel examples of integrable quadratic vector fields for which Kahanʼs
discretization method preserves integrability. Our examples include generalized Suslov and …

In this paper, we present two different approaches for constructing reduced‐order models
(ROMs) for the two‐dimensional shallow water equation (SWE). The first one is based on the …

We present a new numerical algorithm for the solution of coupled collisional and
collisionless systems, based on the block structured adaptive mesh and time refinement …

We show that the decay of strongly excited oscillons in a single vacuum model reveals a
chaotic, fractal-like pattern very much like the one found in kink-antikink collisions in the ϕ 4 …