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:

$r(t+\delta t)=r(t)+\delta tv\left(t+{\frac {1}{2}}\delta t\right)$

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. 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)