We first prove the second order convergence of the Strang-type splitting scheme for the nonlinear Schrödinger equation. The proof does not require commutator estimates but crucially relies on an integral representation of the scheme. It reveals the connection between Strang-type splitting and the midpoint rule. We then show that the integral representation idea can also be used to study the sto...

We develop and demonstrate a computationally efficient numerical splitting technique for solving the reaction–diffusion equation. The scheme is based on the Strang splitting technique wherein the portions of the governing equations containing stiff chemical reaction terms are separated from those parts containing the less-stiff transport terms. As demonstrated, the scheme achieves second-order ...

Climate change causes species range shifts and potentially alters biological invasions. The invasion of European earthworm species across northern North America has severe impacts on native ecosystems. Given the long and cold winters in that region that to date supposedly have slowed earthworm invasion, future warming is hypothesized to accelerate earthworm invasions into yet non-invaded region...

we consider the bifurcation of periodic solutions from an equilibrium point of the given equation: x =f(x,?) , where x ? r , ? is a vector of real parameters ? , ? , ... , ? and f:r x r ->r has at least second continuous derivations in variables

We show that Horrock’s criterion for the splitting of vector bundles on Pn can be extended to vector bundles on multiprojective spaces and to smooth projective varieties with the weak CM property (see Definition 3.11). As a main tool we use the theory of n-blocks and Beilinson’s type spectral sequences. Cohomological characterizations of vector bundles are also showed.

We prove a perturbation (pasting) lemma for conservative (and symplectic) systems. This allows us to prove that C volume preserving vector fields are C-dense in C volume preserving vector fields. Moreover, we obtain that C robustly transitive conservative flows in threedimensional manifolds are Anosov and we conclude that there are no geometrical Lorenz-like sets for conservative flows. Also, b...

Past global change studies have identified changes in species diversity as a major mechanism regulating temporal stability of production, measured as the ratio of the mean to the standard deviation of community biomass. However, the dominant plant functional group can also strongly determine the temporal stability. Here, in a grassland ecosystem subject to 15 years of experimental warming and h...

We discuss the construction of volume-preserving splitting methods based on a tensor product of single-variable basis functions. The vector field is decomposed as the sum of elementary divergence-free vector fields (EDFVFs), each of them corresponding to a basis function. The theory is a generalization of the monomial basis approach introduced in Xue & Zanna (2013, BIT Numer. Math., 53, 265–281...