
MINISYMPOSIA 
Jan
Verwer Memorial Minisymposium, I
Organized
by Christopher Budd

SPEAKERS 

Jason
Frank,
CMU & University of Amsterdam 

Martin
Berzins, University of Utah

Rethinking
Scientific Computing Software for PostPetascale.
The
raw compute power used in the largest machines inceases by a factor
of a thousand every decade and translates into similar increases
at local level. The likely evolution of computer architectures
poses considerable challanges for scientific computing software,
both in the scale of parallelism and its heterogenous nature.
In this talk we consider how adaptive mesh refinement algorithms
and software has has to evolve to run of some of the largest machines
available today and how the software will continue to evolve to
meet future challenges.

John
Butcher, University of Auckland 
Sixty
years of stiff solvers
The seminal paper of Curtiss and Hirschfelder was communicated to
the Proceedings of the National Academy of Sciences in 1951 and
published in the following year. The use of the backward Euler method,
which can be regarded as the first stiff solver, was advocated as
a stable alternative to the forward Euler method. Techniques for
obtaining stable, accurate and efficient solutions to stiff problems
have become an important field of research in many institutions
and laboratories throughout the world, not least being in the work
of Jan Verwer and his colleagues at the CWI. This talk will not
attempt to survey the enormous history of this subject but will
give an account of some items from this history of interest to the
author. 
Jim
Verner,
Simon Fraser University 
A
Retrospective on the Derivation of Explicit RungeKutta Pairs
(slides of talk)
To improve the efficiency of estimating solutions to initial value
problems in ordinary differential equations C. Runge and W. Kutta
designed a recursive evaluation approach to obtaining estimates
within a {\it step} that led to a highorder polynomial approximation
(18951905). As Kutta had difficulty with obtaining correct coefficients
of a method of order 5, a mathematical approach to tabulating and
solving the polynomial order conditions evolved, primarily after
1957. Although Butcher's proposal of 'simplifying conditions' led
to new families of methods, solution of the order conditions remained
a challenge. The proposal to provide a pair of RK approximations
to control the stepbystep error increased this complexity. Yet,
Butcher's "Algebraic Theory of Integration Methods" and
new pairs up to orders 8,9 found by Fehlberg motivated new approaches,
and derivation of better RungeKutta pairs. This talk will survey
some of the strategies used since 1970 to find new formulas, and
will suggest how these tools may be applied to finding algorithms
of different structures or for different problems.

