ChesterRep Collection:
http://hdl.handle.net/10034/6981
Thu, 25 Aug 2016 13:11:51 GMT2016-08-25T13:11:51ZAddendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line
http://hdl.handle.net/10034/617231
Title: Addendum to the article: On the Dirichlet to Neumann Problem for the 1-dimensional Cubic NLS Equation on the Half-Line
Authors: Antonopoulou, Dimitra; Kamvissis, Spyridon
Abstract: We present a short note on the extension of the results of [1] to the case of non-zero
initial data. More specifically, the defocusing cubic NLS equation is considered on the half-line
with decaying (in time) Dirichlet data and sufficiently smooth and decaying (in space) initial data.
We prove that for this case also, and for a large class of decaying Dirichlet data, the Neumann
data are sufficiently decaying so that the Fokas unified method for the solution of defocusing NLS is applicable.
Description: This is an author-created, un-copyedited version of an article accepted for publication in Nonlinearity. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at [forthcoming].Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6172312016-01-01T00:00:00ZStability analysis of a continuous model of mutualism with delay dynamics
http://hdl.handle.net/10034/609519
Title: Stability analysis of a continuous model of mutualism with delay dynamics
Authors: Roberts, Jason A.; Joharjee, Najwa G.
Abstract: In this paper we introduce delay dynamics to a coupled system of
ordinary differential equations which represent two interacting species
exhibiting facultative mutualistic behaviour. The delays are represen-
tative of the beneficial effects of the indirect, interspecies interactions
not being realised immediately. We show that the system with delay
possesses a continuous solution, which is unique. Furthermore we show
that, for suitably-behaved, positive initial functions that this unique
solution is bounded and remains positive, i.e. both of the components
representing the two species remain greater than zero. We show that
the system has a positive equilibrium point and prove that this point
is asymptotically stable for positive solutions and that this stability
property is not conditional upon the delays.Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10034/6095192016-05-01T00:00:00ZError estimates of a high order numerical method for solving linear fractional differential equations
http://hdl.handle.net/10034/609518
Title: Error estimates of a high order numerical method for solving linear fractional differential equations
Authors: Li, Zhiqiang; Yan, Yubin; Ford, Neville J.
Abstract: In this paper, we first introduce an alternative proof of the error estimates of the numerical methods
for solving linear fractional differential equations proposed in Diethelm [6] where a first-degree compound
quadrature formula was used to approximate the Hadamard finite-part integral and the convergence order
of the proposed numerical method is O(∆t 2−α ), 0 < α < 1, where α is the order of the fractional derivative
and ∆t is the step size. We then use the similar idea to prove the error estimates of a high order numerical
method for solving linear fractional differential equations proposed in Yan et al. [37], where a second-degree
compound quadrature formula was used to approximate the Hadamard finite-part integral and we show that
the convergence order of the numerical method is O(∆t 3−α ), 0 < α < 1. The numerical examples are given
to show that the numerical results are consistent with the theoretical results.Fri, 29 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10034/6095182016-04-29T00:00:00ZEdge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes
http://hdl.handle.net/10034/609023
Title: Edge-based nonlinear diffusion for finite element approximations of convection–diffusion equations and its relation to algebraic flux-correction schemes
Authors: Barrenechea, Gabriel; Burman, Erik; Karakatsani, Fotini
Abstract: For the case of approximation of convection–diffusion equations using
piecewise affine continuous finite elements a new edge-based nonlinear diffusion
operator is proposed that makes the scheme satisfy a discrete maximum principle.
The diffusion operator is shown to be Lipschitz continuous and linearity preserving.
Using these properties we provide a full stability and error analysis, which, in the diffusion
dominated regime, shows existence, uniqueness and optimal convergence. Then
the algebraic flux correction method is recalled and we show that the present method
can be interpreted as an algebraic flux correction method for a particular definition of
the flux limiters. The performance of the method is illustrated on some numerical test
cases in two space dimensions.Sat, 07 May 2016 00:00:00 GMThttp://hdl.handle.net/10034/6090232016-05-07T00:00:00Z