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Next: 4.2.5 Symplectic Algorithms Up: 4.2 Initial Value Problems Previous: 4.2.3 Nordsieck Formulation of

4.2.4 Runge-Kutta Method for 2nd order ODE

{\bf 4th order RK for velocity independent forces:}\\
...lta t)^{2}}{6}
[b_{1}+b_{2}+b_{3}]+O[(\Delta t)^{5}]
\nonumber \end{eqnarray}}}

{\bf 4th order RK for velocity dependent forces:}\\
If ...
...lta t)^{2}}{6}
[b_{1}+b_{2}+b_{3}]+O[(\Delta t)^{5}]
\nonumber \end{eqnarray}}

Advantages of RK:

- Self-starting
- Adjustable time steps

But: Repeated evaluation of the acceleration $b(y)$ in a single time step

Franz J. Vesely Oct 2005
See also:
"Computational Physics - An Introduction," Kluwer-Plenum 2001