Verlet leap-frog algorithm

The Verlet leap-frog algorithm is a variant of the original Verlet scheme for use in molecular dynamics simulations. The algorithm is given by:

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 (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 v \left(t+ \frac{1}{2} \delta t\right) = v\left(t - \frac{1}{2} \delta t\right) + \delta t a (t)}

where r is the position, v is the velocity, a is the acceleration and t is the time. 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 \delta t} is known as the time step.

See also

• Velocity Verlet algorithm

References

Related reading

• R. W. Hockney, Methods in Computational Physics vol. 9, Academic Press, New York pp. 135–211 (1970)
• Michel A. Cuendet and Wilfred F. van Gunsteren "On the calculation of velocity-dependent properties in molecular dynamics simulations using the leapfrog integration algorithm", Journal of Chemical Physics 127 184102 (2007)