• Bifurcations in numerical methods for volterra integro-differential equations

      Edwards, John T.; Ford, Neville J.; Roberts, Jason A. (World Scientific Publishing Company, 2003)
      This article discusses changes in bifurcations in the solutions. It extends the work of Brunner and Lambert and Matthys to consider other bifurcations.
    • Boundedness and stability of solutions to difference equations

      Edwards, John T.; Ford, Neville J. (Elsevier Science, 2002-03-01)
      This article discusses the qualitative behaviour of solutions to difference equations, focusing on boundedness and stability of solutions. Examples demonstrate how the use of Lipschintz constants can provide insights into the qualitative behaviour of solutions to some nonlinear problems.
    • Boundness and stability of differential equations

      Edwards, John T.; Ford, Neville J. (Manchester Centre for Computational Mathematics, 2003-05-23)
      This paper discusses the qualitative behaviour of solutions to difference equations, focusing on boundedness and stability of solutions. Examples demonstrate how the use of Lipschintz constants can provide insights into the qualitative behaviour of solutions to some nonlinear problems.
    • A genetic-algorithm approach to simulating human immunodeficiency virus evolution reveals the strong impact of multiply infected cells and recombination

      Bocharov, Gennady; Ford, Neville J.; Edwards, John T.; Breinig, Tanja; Wain-Hobson, Simon; Meyerhans, Andreas; Institute of Numerical Mathematics, Russian Academy of Sciences ; University of Chester ; University of Chester ; University of the Saarland ; Unité de Rétrovirologie Moléculaire, Institut Pasteur ; University of the Saarland (Society for General Microbiology / High Wire Press, 2005-11-01)
      It has been previously shown that the majority of human immunodeficiency virus type 1 (HIV-1)-infected splenocytes can harbour multiple, divergent proviruses with a copy number ranging from one to eight. This implies that, besides point mutations, recombination should be considered as an important mechanism in the evolution of HIV within an infected host. To explore in detail the possible contributions of multi-infection and recombination to HIV evolution, the effects of major microscopic parameters of HIV replication (i.e. the point-mutation rate, the crossover number, the recombination rate and the provirus copy number) on macroscopic characteristics (such as the Hamming distance and the abundance of n-point mutants) have been simulated in silico. Simulations predict that multiple provirus copies per infected cell and recombination act in synergy to speed up the development of sequence diversity. Point mutations can be fixed for some time without fitness selection. The time needed for the selection of multiple mutations with increased fitness is highly variable, supporting the view that stochastic processes may contribute substantially to the kinetics of HIV variation in vivo.
    • Numerical analysis of a singular integral equation

      Diogo, Teresa; Edwards, John T.; Ford, Neville J.; Thomas, Sophy M.
      This preprint discusses the numerical analysis of an integral equation to which convential analytical and numerical theory does not apply.
    • Numerical approaches to bifurcations in solutions to integro-differential equations

      Edwards, John T.; Ford, Neville J.; Roberts, Jason A. (Lea Press, 2002)
      This conference paper discusses the qualitative behaviour of numerical approximations of a carefully chosen class of integro-differential equations of the Volterra type. The results are illustrated with some numerical experiments.
    • The numerical solution of linear multi-term fractional differential equations: Systems of equations

      Edwards, John T.; Ford, Neville J.; Simpson, A. Charles (Elsevier, 2002-11-15)
      This article discusses how the numerical approximation of a linear multi-term fractional differential equation can be calculated by the reduction of the problem to a system of ordinary and fractional differential equations each of order at most unity.
    • Solution map methods for stability analysis of linear and nonlinear Volterra difference equations

      Edwards, John T.; Ford, Neville J. (Institute of Applied Science & Computations, 2004)