ChesterRep Collection:
http://hdl.handle.net/10034/6981
Fri, 01 Jul 2016 07:57:45 GMT2016-07-01T07:57:45ZStability 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.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6095192016-01-01T00:00:00ZError 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, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6095182016-01-01T00:00:00ZEdge-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/10034/6090232016-05-07T00:00:00ZOn the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control
http://hdl.handle.net/10034/600672
Title: On the quenching of a nonlocal parabolic problem arising in electrostatic MEMS control
Authors: Kavallaris, Nikos I.; Lacey, Andrew A.; Nikolopoulos, Christos V.
Abstract: We consider a nonlocal parabolic model for a micro-electro-mechanical system.
Specifically, for a radially symmetric problem with monotonic initial
data, it is shown that the solution quenches, so that touchdown occurs
in the device, in a situation where there is no steady state. It is also
shown that quenching occurs at a single point and a bound on the approach
to touchdown is obtained. Numerical simulations illustrating the results
are given.Sun, 28 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10034/6006722016-02-28T00:00:00Z