ChesterRep Collection:
http://hdl.handle.net/10034/6981
Wed, 26 Oct 2016 00:16:39 GMT2016-10-26T00:16:39ZIntroducing delay dynamics to Bertalanffy's spherical tumour growth model
http://hdl.handle.net/10034/620218
Title: Introducing delay dynamics to Bertalanffy's spherical tumour growth model
Authors: Roberts, Jason A.; Themairi, Asmaa A.
Abstract: We introduce delay dynamics to an ordinary differential equation model of tumour growth based upon von Bertalanffy's growth model, a model which has received little attention in comparison to other models, such as Gompterz, Greenspan and logistic models. Using existing, previously published data sets we show that our delay model can perform better than delay models based on a Gompertz, Greenspan or logistic formulation. We look for replication of the oscillatory behaviour in the data, as well as a low error value (via a Least-Squares approach) when comparing. We provide the necessary analysis to show that a unique, continuous, solution exists for our model equation and consider the qualitative behaviour of a solution near a point of equilibrium.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6202182016-01-01T00:00:00ZFourier spectral methods for some linear stochastic space-fractional partial differential equations
http://hdl.handle.net/10034/620201
Title: Fourier spectral methods for some linear stochastic space-fractional partial differential equations
Authors: Liu, Yanmei; Khan, Monzorul; Yan, Yubin
Abstract: Fourier spectral methods for solving some linear stochastic space-fractional partial differential
equations perturbed by space-time white noises in one-dimensional case are introduced and analyzed.
The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of Laplacian subject
to some boundary conditions. We approximate the space-time white noise by using piecewise constant
functions and obtain the approximated stochastic space-fractional partial differential equations. The
approximated stochastic space-fractional partial differential equations are then solved by using Fourier
spectral methods. Error estimates in $L^{2}$- norm are obtained. Numerical examples are given.Fri, 01 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10034/6202012016-07-01T00:00:00ZNumerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh-Nagumo equation
http://hdl.handle.net/10034/619088
Title: Numerical investigation of noise induced changes to the solution behaviour of the discrete FitzHugh-Nagumo equation
Authors: Ford, Neville J.; Lima, Pedro M.; Lumb, Patricia M.
Abstract: In this work we introduce and analyse a stochastic functional equation, which contains both delayed and
advanced arguments. This equation results from adding a stochastic term to the discrete FitzHugh-Nagumo
equation which arises in mathematical models of nerve conduction. A numerical method is introduced
to compute approximate solutions and some numerical experiments are carried out to investigate their
dynamical behaviour and compare them with the solutions of the corresponding deterministic equation.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6190882016-01-01T00:00:00ZQuenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
http://hdl.handle.net/10034/618944
Title: Quenching solutions of a stochastic parabolic problem arising in electrostatic MEMS control
Authors: Kavallaris, Nikos I.
Abstract: In the current paper, we consider a stochastic parabolic equation which actually serves as a mathematical model describing the operation of an electrostatic actuated micro-electro-mechanical system (MEMS). We first present the derivation of the mathematical model. Then after establishing the local well-posedeness of the problem we investigate under which circumstances a {\it finite-time quenching} for this SPDE, corresponding to the mechanical phenomenon of {\it touching down}, occurs. For that purpose the Kaplan's eigenfunction method adapted in the context of SPDES is employed.Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10034/6189442016-01-01T00:00:00Z