Leapfrog integration

Leapfrog integration

Leapfrog integration is a simple method for integrating differential equations.

Leapfrog integration is equivalent to calculating positions and velocities alternately, at alternate time points, so that they 'leapfrog' over each other.

Leapfrog integration is a second order method hence usually works better than Euler integration which is only first order.

The equations for leapfrog integration can be written:

:x_{i+1} = x_i + v_i, dt + a_i, frac{dt^2}{2}

:v_{i+1} = v_i + frac{a_i + a_{i+1{2},dt. [ [http://www.artcompsci.org/vol_1/v1_web/node34.html 4.1 Two Ways to Write the Leapfrog ] ]

References

ee also

*Numerical ordinary differential equations
*Euler integration
*Verlet integration
*Runge kutta integration


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