The fourth-order Runge-Kutta method is a numerical technique used to solve ordinary differential equations. It provides a way to approximate the solution by evaluating the function at several points within each step, leading to greater accuracy compared to simpler methods. This method involves calculating four intermediate slopes, or "k-values," for each step. These slopes are then combined to produce a weighted average, which determines the next value in the solution. The fourth-order Runge-Kutta method is widely used in various fields, including physics, engineering, and computer science, due to its balance of accuracy and computational efficiency.