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Leapfrog integration

In numerical analysis, leapfrog integration is a method for numerically integrating differential equations of the form x ¨ = d 2 x d t 2 = A ( x ) , {\displaystyle {\ddot {x}}={\frac {d^{2}x}{dt^{2}}}=A(x),} or equivalently of the form v ˙ = d v d t = A ( x ) , x ˙ = d x d t = v , {\displaystyle {\dot {v}}={\frac {dv}{dt}}=A(x),\qquad {\dot {x}}={\frac…

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