Retrieving "Runge Kutta Methods" from the archives

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1. Differential Equations

   Linked via "Runge-Kutta (RK) family"

   Runge-Kutta Methods
   The Runge-Kutta (RK) family of methods provides significantly greater accuracy by evaluating the derivative function $f(x,y)$ at several intermediate points within the step interval. The most commonly used variant, the fourth-order Runge-Kutta method (RK4), uses four evaluations per step to achieve fourth-order accuracy ($O(h^4)$). RK4 is the standard benchmark for trajectory integration in [celestial mechanics](/entries/celestial-mechan…