The third-order Runge-Kutta formula is given by [vec{X}_{i+1}=vec{X}_{i}+frac{1}{6}left(vec{K}_{1}+4 vec{K}_{2}+vec{K}_{3} ight)] where [begin{gathered}vec{K}_{1}=h vec{F}left(vec{X}_{i}, t_{i} ight) vec{K}_{2}=h vec{F}left(vec{X}_{i}+frac{1}{2}
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The third-order Runge-Kutta formula is given by
\[\vec{X}_{i+1}=\vec{X}_{i}+\frac{1}{6}\left(\vec{K}_{1}+4 \vec{K}_{2}+\vec{K}_{3}\right)\]
where
\[\begin{gathered}\vec{K}_{1}=h \vec{F}\left(\vec{X}_{i}, t_{i}\right) \\\vec{K}_{2}=h \vec{F}\left(\vec{X}_{i}+\frac{1}{2} \vec{K}_{1}, t_{i}+\frac{1}{2} h\right)\end{gathered}\]
and
\[\vec{K}_{3}=h \vec{F}\left(\vec{X}_{i}-\vec{K}_{1}+2 \vec{K}_{2}, t_{i}+h\right)\]
Using this formula, solve the problem considered in Example 11.2.
Data From Example 11.2:-
Data From Example 11.1:-
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