Department of Mathematics
Title : Extrapolation of symmetrized Runge-Kutta methods
| Speaker: Annie Gorgery Affiliation: Auckland University Time: 12 pm Thursday, 5 April, 2012 Location: 412 |
Abstract
| Gragg introduced smoothing for the explicit two-step midpoint rule to dampen the parasitic oscillatory component arising naturally in the numerical solution. This allowed the development of successful extrapolation algorithms for nonstiff problems. The same smoothing formula could be used for solving stiff problems by the implicit midpoint or trapezoidal rules to dampen the stiff components. This has been successfully exploited by Lindberg, Dahlquist and others in developing extrapolation algorithms for stiff problems. For higher order methods, the generalization of smoothing is known as symmetrization. In this talk, we discuss two ways of applying symmetrization, active and passive, and four ways of subsequently applying extrapolation in the constant stepsize setting. We observe numerically that passive symmetrization with passive extrapolation is more efficient than active symmetrization with active extrapolation. In the variable stepsize setting, there are two ways of applying extrapolation with symmetrization. We also find that symmetrization can be used for error estimation. In the numerical experiments on the STIFF DETEST problem set, we observe that passive symmetrization with active extrapolation is more efficient than active symmetrization with active extrapolation. In summary, our work shows that extrapolation algorithms can be developed that are based on high order symmetric Runge-Kutta methods with appropriate use of symmetrization. |
-
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
