Dynamical Systems
The Runge-Kutta method is a family of iterative techniques used for solving ordinary differential equations (ODEs), offering a more accurate alternative to simpler methods like Euler's method. These methods are designed to approximate the solutions of ODEs by using a series of intermediate calculations, which help improve precision without requiring smaller step sizes. The most common version, known as the fourth-order Runge-Kutta method, strikes a balance between computational efficiency and accuracy, making it widely applicable in various fields such as physics, engineering, and mathematics.
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