• A novel approach to rigid spheroid models in viscous flows using operator splitting methods 

      Tapley, Benjamin; Celledoni, Elena; Owren, Brynjulf; Andersson, Helge Ingolf (Peer reviewed; Journal article, 2019)
      Calculating cost-effective solutions to particle dynamics in viscous flows is an important problem in many areas of industry and nature. We implement a second-order symmetric splitting method on the governing equations for ...
    • Symplectic integration of PDEs using Clebsch variables 

      McLachlan, Robert I.; Offen, Christian; Tapley, Benjamin (Journal article, 2019)
      Many PDEs (Burgers' equation, KdV, Camassa-Holm, Euler's fluid equations, …) can be formulated as infinite-dimensional Lie-Poisson systems. These are Hamiltonian systems on manifolds equipped with Poisson brackets. The ...
    • Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps 

      Celledoni, Elena; Evripidou, Charalambos; McLaren, David I.; Owren, Brynjulf; Quispel, Gilles Reinout Willem; Tapley, Benjamin; van der Kamp, Peter H. (Peer reviewed; Journal article, 2019)
      In this letter we propose a systematic approach for detecting and calculating integrals and preserved measures of rational maps. The approach is based on the use of cofactors and discrete Darboux polynomials and relies on ...