The business of myth-making: Mary Poppins, P.L. Travers and the Disney effect

In just one of the many extraordinary moments during the spectacular Opening Ceremony of the 2012 London Olympic Games, thirty Mary Poppinses floated into the stadium on their umbrellas to battle a 40 foot-long inflatable Lord Voldemort. This multi-million pound extravaganza was telecast to a global audience of over one billion people, highlighting in an extremely effective manner the grandeur and eccentricities of the host nation, and featuring uniquely British icons such as Mr Bean, James Bond, The Beatles and Harry Potter, as well as those quintessential icons of Englishness, the Royal Family, double-decker red buses and the National Health Service.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.