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

      Pal, Kamal; Liu, Fang; Yan, Yubin; Roberts, Graham; University of Chester (Springer International Publishing, 2015-06-17)
      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.
    • Numerical Solutions of Fractional Differential Equations by Extrapolation

      Pal, Kamal; Liu, Fang; Yan, Yubin; University of Chester (Springer International Publishing, 2015-06-17)
      An extrapolation algorithm is considered for solving linear fractional differential equations in this paper, which is based on the direct discretization of the fractional differential operator. Numerical results show that the approximate solutions of this numerical method has the expected asymptotic expansions.
    • Using and Validating Airborne Ultrasound as a Tactile Interface within Medical Training Simulators

      Hung, Gary M. Y.; John, Nigel W.; Hancock, Chris; Hoshi, Takayuki; University of Chester (Springer International Publishing, 2014-10)
      We have developed a system called UltraSendo that creates a force field in space using an array of ultrasonic transducers cooperatively emitting ultrasonic waves to a focal point. UltraSendo is the first application of this technology in the context of medical training simulators. A face validation study was carried out at a Catheter Laboratory in a major regional hospital.