The Runge-Kutta formula is a powerful set of iterative methods used for solving ordinary differential equations (ODEs) by approximating the solutions at discrete points. These methods improve the accuracy of numerical solutions through multiple evaluations of the derivative at each step, allowing for a more precise approximation compared to simpler techniques like Euler's method. The family of Runge-Kutta methods includes several variations, with the most commonly used being the fourth-order method, which strikes a balance between computational efficiency and accuracy.
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