Im Wald    -    In the forest

Here we are in the darkest forest.
This forest consists of nothing but different Nyström trees. Consider the numerical solution of a initial value problem (IVP) for the system of second-order differential equations:
y'' = f(x,y),    y(xo) = yo  and   y'(xo) = y'o.
A Nyström tree is an equation of condition for the
explicit Runge-Kutta-Nyström(RKN)-type methods.
The most efficient numerical methods
The scientific community seems to be agreed that the explicit RKN-types are the most efficient methods for solving the IVP. On this website I present the best RKN-type methods I had made in [0]. They are mentioned in [1], but are not yet published. In [4] there is published this forest. In [8] J. Becker explains his computer program for generating trees.

© 6. Januar 2002, Josef Gräf, Im Wald