The Runge-Kutta 4th order method is a numerical technique used to solve ordinary differential equations. It provides an approximate solution by calculating the value of a function at successive points, using weighted averages of slopes. This method is particularly effective for problems where analytical solutions are difficult or impossible to obtain. In each step, the Runge-Kutta 4th order method evaluates the function at four different points, combining these evaluations to produce a more accurate estimate of the function's value. This approach improves precision compared to simpler methods, making it a popular choice in fields such as physics, engineering, and computer science.