Which describes the Runge-Kutta method?

The Runge-Kutta method refers to a family of numerical techniques used to solve ordinary differential equations (ODEs). These methods provide approximate solutions to initial value problems by discretizing the ODEs and computing successive points in the solution curve. The most commonly known version is the fourth-order Runge-Kutta method, which improves accuracy by taking multiple sample points within each step, allowing for better estimates of the solution's behavior.

This method is particularly valuable for problems where analytical solutions may be difficult or impossible to obtain, making it a fundamental tool in engineering and applied mathematics. It is widely utilized due to its effectiveness and relatively simple implementation compared to other numerical methods for solving ODEs.