The second-order Runge-Kutta formula is given by [vec{X}_{i+1}=vec{X}_{i}+frac{1}{2}left(vec{K}_{1}+vec{K}_{2} ight)] where [vec{K}_{1}=h vec{F}left(vec{X}_{i}, t_{i} ight) quad text {

The second-order Runge-Kutta formula is given by

\[\vec{X}_{i+1}=\vec{X}_{i}+\frac{1}{2}\left(\vec{K}_{1}+\vec{K}_{2}\right)\]

where

\[\vec{K}_{1}=h \vec{F}\left(\vec{X}_{i}, t_{i}\right) \quad \text { and } \quad \vec{K}_{2}=h \vec{F}\left(\vec{X}_{i}+\vec{K}_{1}, t_{i}+h\right)\]

Using this formula, solve the problem considered in Example 11.2.