Verlet leap-frog algorithm

The Verlet leap-frog algorithm is a variant of the original Verlet scheme (Ref. 1)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r(t + \delta t) = r (t) + \delta t v\left(t+ \frac{1}{2} \delta t\right)}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle v\left(t+{\frac {1}{2}}\delta t\right)=v\left(t-{\frac {1}{2}}\delta t\right)+\delta ta(t)}

where r is the position, v is the velocity, a is the acceleration and t is the time.

See also

• Velocity Verlet algorithm

References

1. Loup Verlet "Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules", Physical Review 159 pp. 98 - 103 (1967)
2. R. W. Hockney, Methods in Computational Physics vol. 9, Academic Press, New York pp. 135–211 (1970)