Seminar Abstract:

A classical nonlinear PDE used for modelling heat transfer between concentric cylinders by fluid convection and also for modelling porous flow can be solved by hand using a loworder perturbation method. Extending this solution to higher order using computer algebra is surprisingly hard owing to exponential growth in the size of the series terms, naively computed. In the mid1990's, socalled "Large Expression Management" tools were invented to allow construction and use of socalled "computation sequences" or "straightline programs" to extend the solution to 11th order. The cost of the method was O(N^8) in memory, high but not exponential. Twenty years of doubling of computer power allows this method to get 15 terms. A new method, which reduces the memory cost to O(N^4), allows us to compute to N=30. At this order, singularities can reliably be detected using the quotientdifference algorithm. This allows confident investigation of the solutions, for different values of the Prandtl number.
This work is joint with Yiming Zhang (PhD Oct 2013).
