Identify one method for solving ordinary differential equations (ODEs).

The Runge-Kutta method is a powerful numerical technique used for solving ordinary differential equations (ODEs). It is particularly significant because it provides a systematic way to obtain approximate solutions for ODEs that may not be easily solvable using analytical methods. The method includes a family of algorithms, with the most commonly used being the fourth-order Runge-Kutta method, which achieves a good balance between computational efficiency and accuracy.

The strength of the Runge-Kutta method lies in its ability to use multiple sampling points within each time step to calculate an average slope, leading to more accurate results. By combining these slopes appropriately, the method can produce an estimate of the solutions at subsequent points in the solution space.

In terms of general applicability, the Runge-Kutta method can be used for a wide range of initial value problems, making it a versatile and essential tool in engineering and scientific computation involving ODEs.