The basic idea behind Runge-Kutta methods is to approximate the solution of an ODE by iteratively improving upon an initial guess. The most commonly used version is the fourth-order Runge-Kutta method (RK4), which provides a good balance between accuracy and computational efficiency. The RK4 method involves calculating intermediate values (called "k-values") at various points within each step, and then combining them to produce a more accurate estimate of the solution.
