a) Using Runge-Kutta of $4^{\text{th}}$ order, compute $y(0.4)$, give…

Question

a) Using Runge-Kutta of $4^{\text{th}}$ order, compute $y(0.4)$, given that $\frac{dy}{dx} = \frac{y^2 - x^2}{y^2 + x^2}$, $y(0) = 1$ and $h = 0.2$.

b) Find the first and second derivatives of $y$ at $x = 1.5$ for the following data:

\begin{tabular}{c|cccccc}

$x$ & 1.5 & 2 & 2.5 & 3 & 3.5 & 4 \\

\hline

$y$ & 3.375 & 7 & 13.625 & 24 & 38.875 & 59

\end{tabular}

c) Find the $8^{\text{th}}$ and the general term of the series: $0, 12, 51, 132, 270, 480, \dots\dots\dots$

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• Runge-Kutta Method — topic
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