Department of Mathematics
Title : Variable order and stepsize for numerical integrators
| Speaker: Professor John Butcher Affiliation: Auckland University Time: 12 pm Thursday, 26 April, 2012 Location: 412 |
Abstract
| For classical numerical methods for ordinary differential equations, there are inherent difficulties in constructing efficient and reliable variable order and variable stepsize algorithms. Denote by h the current stepsize and p the order of the current step. In the case of Runge-Kutta methods, for example, embedding is not able to provide asymtotically correct error estimates at a moderate cost. On the other hand, for linear multistep methods, the difficulties lie in the need to interpolate and reorganize the data when a variation of h or p is called for. Many of these difficulties can be overcome in the case of multistep-multivalue, or general linear, methods. The underlying idea is the use of a Lagrange multiplier formulation to provide a rational process for choosing among competing p and selecting the optimal h value. A second underlying idea is the use of the so-called `scale and modify technique to guarantee smooth transitions between one step and the next, even though h, and possibly also p, has been adjusted. |
-
Programmes and Centres
- New Zealand Institute of Mathematics and its Applications (NZIMA)
- Community for Understanding and Learning in the Mathematical Sciences (CULMS)
- Centre for Mathematical Social Science (CMSS)
- Department of Computer Science
- Department of Engineering Science
- Department of Physics
- Department of Statistics
- Auckland Bioengineering Institute
