Graduate Seminar - 3/06, 12:00PM Duncan Hall 1064

Reid Atcheson

"Challenging Conventional Wisdom on Time-Stepping"

Conventional wisdom on time-stepping linear differential equations suggests that if your system is stiff then an implicit time-stepping method may be the more appropriate choice of solution technique, owing to their favorable stability properties. In this talk I will reveal that equipped with just a little bit more knowledge of the problem, possibly coming from underlying physics, an explicit method can be made equally as competitive. I will provide examples of differential equations coming from different types of physical problems and in each case providing a fully explicit method which performs competitively to an implicit method. Furthermore I will show that for linear problems an implicit method coupled with an iterative solver can be thought of as an explicit method, and in reverse an explicit method can be thought of as a Krylov iterative method for the solution of linear equations. In essence this will suggest that implicit methods per se do not have a built-in advantage over explicit methods on stiff problems. Their use however may still be more appropriate, and I will discuss how to choose between the two in detail.