What characterizes the Runge-Kutta method?

The Runge-Kutta method is characterized as a family of methods for solving ordinary differential equations (ODEs). This approach encompasses a range of techniques that yield approximate solutions to initial value problems involving ODEs.

The strength of the Runge-Kutta methods lies in their ability to achieve higher accuracy by taking multiple evaluation points within each step of the calculation, rather than relying on a single point, as seen in simpler methods like Euler's method. This increases the precision of the approximation for the solution of the differential equations.

Runge-Kutta methods are versatile and can be applied to both linear and nonlinear equations, thus making them more broadly applicable than methods restricted to linear equations only. They are not focused on graphical representations; rather, they concentrate on numerical solutions of differential equations, which is fundamental for many engineering and applied science problems.