**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.