Semi-implicit Euler method: Difference between revisions

Revision as of 17:15, 6 July 2018

Revision as of 21:03, 30 July 2018

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\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 ==