Stability of Runge-Kutta Methods for Trajectory Problems |
| |
Authors: | COOPER G J |
| |
Institution: |
School of Mathematical and Physical Sciences, The University of Sussex Brighton, BN1 9QH
|
| |
Abstract: | A solution of a system of m autonomous differential equationsdefines a trajectory in m-dimensional space and, in particular,may give a closed orbital path. Typical trajectories are describedby a model nonlinear problem introduced in this article. Forthis problem, a trajectory lies on a surface characterized bya real symmetric matrix. It is shown that some Runge-Kutta methodspossess a property which ensures that, for this model problem,the numerical solution lies on the same surface as the trajectory.When m = 2, the numerical solution lies on the trajectory. Thisproperty is related to algebraic stability. A weaker propertysuffices for normalized differential systems. |
| |
Keywords: | |
本文献已被 Oxford 等数据库收录! |
|