Runge-Kutta Methods
A family of iterative numerical integration algorithms used to solve ordinary differential equations with high accuracy.
Governing formula
RK4: y_(n+1) = y_n + (h / 6) (k₁ + 2 k₂ + 2 k₃ + k₄)
SI unit
Numerical ODE Integration Method
In depth
Fourth-order Runge-Kutta (RK4) evaluates derivatives at four intermediate trial steps per time step h, achieving high accuracy with local error O(h⁵) and global error O(h⁴) without computing higher derivatives.
Examples in the real world
Integrating planetary orbital trajectories and N-body gravitational simulations.