95 citations · 247 across the 7 of their papers we have counts for
7 papers
A unification of least-squares and Green-Gauss gradients under a common projection-based gradient reconstruction framework
Alexandros Syrakos, Oliver Oxtoby, Eugene de Villiers +3
We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections,…
A family of first-order accurate gradient schemes for finite volume methods
Oliver Oxtoby, Alexandros Syrakos, Eugene de Villiers +3
A new discretisation scheme for the gradient operator, suitable for use in second-order accurate Finite Volume Methods (FVMs), is proposed. The derivation of this scheme, which we…
Wobbling kinks in theory
I. V. Barashenkov, O. F. Oxtoby
We present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode. The long-range behaviour of the radiation is described by matchin…
Asymptotic expansion of the wobbling kink
O F Oxtoby, I V Barashenkov
The method of multiple scales is used to study the wobbling kink of the equation. The amplitude of the wobbling is shown to decay very slowly, as , and hence the wo…
Moving solitons in the discrete nonlinear Schrödinger equation
O. F. Oxtoby, I. V. Barashenkov
Using the method of asymptotics beyond all orders, we evaluate the amplitude of radiation from a moving small-amplitude soliton in the discrete nonlinear Schrödinger equation. When…
Translationally invariant discrete kinks from one-dimensional maps
I. V. Barashenkov, O. F. Oxtoby, Dmitry E. Pelinovsky
For most discretisations of the theory, the stationary kink can only be centered either on a lattice site or midway between two adjacent sites. We search for exceptional disc…