leapfrog integration

There are two primary strengths to Leapfrog integration when applied to mechanics problems.

The second strength of Leapfrog integration is its symplectic nature, which implies that it conserves the (slightly modified) energy of dynamical systems.

A second order method is leapfrog integration, but higher-order integration methods such as the Runge-Kutta methods can be employed.

Leapfrog integration is equivalent to updating positions and velocities at interleaved time points, staggered in such a way that they 'leapfrog' over each other.

Space and time steps must satisfy the CFL condition, or the leapfrog integration used to solve the partial differential equation is probable to become unstable.

Leapfrog integration is a second order method, in contrast to Euler integration, which is only first order, yet requires the same number of function evaluations per step.

An iterative process is followed by simulating a pseudo-dynamic process in time, with each iteration based on an update of the geometry, similar to Leapfrog integration and related to Velocity Verlet integration.

Because of its time-reversibility, and because it is a symplectic integrator, leapfrog integration is also used in Hamiltonian Monte Carlo, a method for drawing random samples from a probability distribution whose overall normalization is unknown.

Alternating between the two variants of the semi-implicit Euler method leads in one simplification to the Störmer-Verlet integration and in a slightly different simplification to the leapfrog integration, increasing both the order of the error and the order of preservation of energy.