Date & Time: Wednesday, March 19, 2014, 16:00-17:00.
Venue: Ramanujan Hall

Speaker: Graeme Fairweather, Mathematical Reviews, AMS

Title: Alternating Direction Implicit Orthogonal Spline Collocation Methods for Time-Dependent Problems

Abstract: The formulation, analysis and implementation of efficient numerical techniques for the solution of time-dependent problems in two space variables are described. The basic approach is to discretize in space using orthogonal spline collocation (OSC) (also known as spline collocation at Gauss points), and to advance in time using an alternating direction implicit (ADI) method. OSC has several advantages over finite difference and finite element methods, while an ADI method reduces a multidimensional problem to sets of independent one-dimensional problems in the coordinate directions which can be solved efficiently using existing software.

After an overview of the development of ADI OSC methods for parabolic problems, extensions to partial integro--differential equations and a class of two-component nonlinear reaction-diffusion problems are presented. Numerical results demonstrate the efficacy of the methods.