The Runge-Kutta methods are a family of numerical techniques used to solve ordinary differential equations. They provide a way to approximate the solutions by breaking the problem into smaller steps, allowing for greater accuracy than simpler methods like Euler's method. The most commonly used version is the fourth-order Runge-Kutta method, which calculates intermediate values to improve the estimate of the solution. These methods are widely used in various fields, including physics, engineering, and computer science, due to their effectiveness in handling complex systems. By adjusting the number of steps and the method's order, users can balance accuracy and computational efficiency for their specific needs.