Numerical Method20775 marksNumerical: Newton forward difference interpolationNewton's Interpolation using divided differences, forward di
Newton's Forward Difference Table Construct Newton's forward difference table for the given data points and approximate the value of f(x) at x = 15.
Newton's Forward Difference Table
Construct Newton's forward difference table for the given data points and approximate the value of $f(x)$ at $x = 15$.
$$\begin{array}{c|ccccc} x & 10 & 20 & 30 & 40 & 50 \ \hline F(x) & 0.173 & 0.342 & 0.5 & 0.643 & 0.766 \end{array}$$
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x F(x) --------- 10 0.173 20 0.342 30 0.500 40 0.643 50 0.766 Spacing $h = 10$, $x0 = 10$. Required: $f(15)$. --- First differences ($\Delta$): - $0.342 - 0.173 = 0.169$ - $0.500 - 0.342 = 0.158$ - $0.643 - 0.500 = 0.143$ - $0.766 - 0.643 = 0.123$ Second differences ($\Delta^2$): -