1er Symposium canadien en analyse numérique et calcul scientifique
An ADI orthogonal spline collocation method for nonlinear reaction-diffusion systems on evolving domains
Fairweather, Graeme (1) and Ryan Fernandes (2)
(1) Mathematical Reviews, AMS, (2) The Petroleum Institute

Since their introduction over fifty years ago,  alternating direction implicit (ADI) methods have been employed to solve a variety of time-dependent multidimensional problems.  Their primary attraction is that they reduce such a problem to independent systems of one-dimensional problems.
In this paper, we describe an ADI method for the solution of a class of two-component nonlinear reaction-diffusion problems on evolving domains.  In this method, orthogonal spline collocation (OSC) is used for the spatial discretization, and the time-stepping is done with an algebraically linear ADI method based on an extrapolated Crank-Nicolson OSC method. Numerical results are provided to demonstrate the expected global rates of convergence of the method.

Mercredi, 19 juin, 10h00
Salle Des Plaines B