Summary of the 1994 Meeting

The third meeting in the SCOTTISH COMPUTATIONAL MATHEMATICS SYMPOSIUM (SCMS) series of one-day conferences was held at the University of Strathclyde on 12 September 1994. The conference, which attracted 39 participants, was organised by Dugald Duncan of Heriot-Watt University and John Mackenzie and Dave Sloan of Strathclyde University. Financial support was given by the London Mathematical Society. The aim of the SCMS meetings is to bring together mathematicians and others who use computational methods to solve mathematical problems and to present them with a range of state-of-the-art topics in computational mathematics. At SCMS 94 the topics were presented by four invited lecturers. There was also a demonstration of computer software by Clecom Microcomputer Specialists.

Dr Chris Budd (Bristol) spoke on Self-similarity and adaptive remeshing. He pointed out that many PDEs have similarity solutions and he went on to show that these solutions are often attractors. Numerical methods based on adaptive meshes were shown to have the same invariance properties of the underlying PDEs: they have similarity solutions that appear to be globally attracting. Dr Andy Gardiner (Sussex) considered Phase field computations of solidification of undercooled liquids. The phase field equations consist of two coupled parabolic equations and Andy considered some numerical issues---including front tracking---arising in the solution of the system in one and two spatial dimensions.

Dr Nick Higham (Manchester) set out to show that rounding error analysis can be relatively painless if problems are treated in the right way. He described three common misconceptions of floating point arithmetic. By means of illuminating examples he offered insight into rounding errors associated with inner product evaluation, summation of $n$ numbers and polynomial evaluation. In the course of his discussion of polynomial evaluation Nick described ``running error analysis'', a now neglected technique much used by Wilkinson on the ACE in the 1950s and 1960s. Professor Tito Toro (Manchester Metropolitan) presented the Weighted Average Flux (WAF) approach to the numerical solution of systems of hyperbolic conservation laws. Initially he presented WAF-type schemes for one-dimensional problems, then split versions were introduced for multidimensional problems. A finite volume version of the WAF approach was discussed and strategies for oscillation-free schemes incorporating TVD and TVB concepts were given.