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Subjectsfractional differential equations (2)Affine photometric warping model (1)ageing (1)agents based modelling (1)aging (1)Augmented Reality (AR) (1)Biochar (1)boundary value problems (1)Cardiovascular disease (1)ceramics (1)View MoreAuthorsFord, Neville J. (5)Lawrence, Jonathan (4)Waugh, David G. (4)Lumb, Patricia M. (2)Mc Auley, Mark T. (2)Morgado, Maria L. (2)Southall, Helen (2)Yan, Yubin (2)Aufderheide, Dominik (1)Avdic, Dalila (1)View MoreTypes

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Using approximations to Lyapunov exponents to predict changes in dynamical behaviour in numerical solutions to stochastic delay differential equations

Ford, Neville J.; Norton, Stewart J. (Springer, 2007)

This book chapter explores the parameter values at which there are changes in qualitative behaviour of the numerical solutions to parameter-dependent linear stochastic delay differential equations with multiplicative noise. A possible tool in this analysis is the calculation of the approximate local Lyapunov exponents. We show that estimates for the maximal local Lyapunov exponent have predictable distributions dependent upon the parameter values and the fixed step length of the numerical method, and that changes in the qualitative behaviour of the solutions occur at parameter values that depend on the step length.

A high order numerical method for solving nonlinear fractional differential equation with non-uniform meshes

Fan, Lili; Yan, Yubin (Springer Link, 2019-01-18)

We introduce a high-order numerical method for solving nonlinear fractional differential equation with non-uniform meshes. We first transform the fractional nonlinear differential equation into the equivalent Volterra integral equation. Then we approximate the integral by using the quadratic interpolation polynomials. On the first subinterval $[t_{0}, t_{1}]$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{0}, t_{1}, t_{2}$ and in the other subinterval $[t_{j}, t_{j+1}], j=1, 2, \dots N-1$, we approximate the integral with the quadratic interpolation polynomials defined on the nodes $t_{j-1}, t_{j}, t_{j+1}$. A high-order numerical method is obtained. Then we apply this numerical method with the non-uniform meshes with the step size $\tau_{j}= t_{j+1}- t_{j}= (j+1) \mu$ where $\mu= \frac{2T}{N (N+1)}$. Numerical results show that this method with the non-uniform meshes has the higher convergence order than the standard numerical methods obtained by using the rectangle and the trapzoid rules with the same non-uniform meshes.

Mathematical modelling and numerical simulations in nerve conduction

Ford, Neville J.; Lima, Pedro M.; Lumb, Patricia M. (Scitepress, 2015)

In the present work we analyse a functionaldifferential equation, sometimes known as the discrete FitzHugh-Nagumo equation, arising in nerve conduction theory.

Laser surface engineering of polymeric materials and the effects on wettability characteristics

Waugh, David G.; Avdic, Dalila; Woodham, K. J.; Lawrence, Jonathan (Scrivener/John Wiley & Sons., 2014-12)

Wettability characteristics are believed by many to be the driving force in applications relating to adhesion. So, gaining an in-depth understanding of the wettability characteristics of materials before and after surface treatments is crucial in developing materials with enhanced adhesion properties. This chapter details some of the main competing techniques to laser surface engineering followed by a review of current cutting edge laser surface engineering techniques which are used for wettability and adhesion modulation. A study is provided in detail for laser surface treatment (using IR and UV lasers) of polymeric materials. Sessile drop analysis was used to determine the wettability characteristics of each laser surface treated sample and as-received sample, revealing the presence of a mixed-state wetting regime on some samples. Although this outcome does not follow current and accepted wetting theory, through numerical analysis, generic equations to predict this mixed state wetting regime and the corresponding contact angle are discussed.

Numerical solutions to the solution of some fractional differential equations

Simpson, A. Charles (Lea Press, 2002)

Nonpolynomial approximation of solutions to delay fractional differential equations

Ford, Neville J.; Morgado, Maria L.; Rebelo, Magda S. (University of Oviedo, 2013)

Stability, structural stability and numerical methods for fractional boundary value problems

Ford, Neville J.; Morgado, Maria L. (Birkhauser, 2013)

Finite Difference Method for Two-Sided Space-Fractional Partial Differential Equations

Pal, Kamal; Liu, Fang; Yan, Yubin; Roberts, Graham (Springer International Publishing, 2015-06)

Finite difference methods for solving two-sided space-fractional partial differential equations are studied. The space-fractional derivatives are the left-handed and right-handed Riemann-Liouville fractional derivatives which are expressed by using Hadamard finite-part integrals. The Hadamard finite-part integrals are approximated by using piecewise quadratic interpolation polynomials and a numerical approximation scheme of the space-fractional derivative with convergence order O(Δx^(3−α )),10 , where Δt,Δx denote the time and space step sizes, respectively. Numerical examples are presented and compared with the exact analytical solution for its order of convergence.

Laser surface structuring of ceramics, metals and polymers for biological applications: A review

Shukla, Pratik; Waugh, David G.; Lawrence, Jonathan (Elsevier, 2015)

Laser surface modification of polymeric materials for microbiological applications

Gillett, Alice R.; Waugh, David G.; Lawrence, Jonathan (Elsevier, 2016-04-15)

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