Content deleted Content added
m →References: Task 5: Fix CS1 deprecated coauthor parameter errors |
|||
Line 62:
\end{align}</math>
The iteration preserves the modified energy functional <math>E_h(x,v)=\tfrac12\left(v^2+\omega^2\,x^2-\omega^2\Delta t\,vx\right)</math> exactly, leading to stable periodic orbits (for sufficiently small step size) that deviate by <math>O(\Delta t)</math> from the exact orbits. The exact circular frequency <math>\omega</math> increases in the numerical approximation by a factor of <math>1+\tfrac1{24}\omega^2\Delta t^2+O(\Delta t^4)</math>.
== References ==
| |||