Trees and numerical methods for ordinary differential equations |
| |
Authors: | J C Butcher |
| |
Institution: | 1. The University of Auckland, Auckland, New Zealand
|
| |
Abstract: | This paper presents a review of the role played by trees in the theory of Runge–Kutta methods. The use of trees is in contrast to early publications on numerical methods, in which a deceptively simpler approach was used. This earlier approach is not only non-rigorous, but also incorrect. It is now known, for example, that methods can have different orders when applied to a single equation and when applied to a system of equations; the earlier approach cannot show this. Trees have a central role in the theory of Runge–Kutta methods and they also have applications to more general methods, involving multiple values and multiple stages. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|