GATE Civil Engineering (CE) 2020 Shift 1 Solved Paper

Question : 40 of 65

Marks: +1, -0

A continuous function/ft) is defined. If the third derivative at

x

, is to be computed by using the fourth order central finite-divided-difference scheme (with step length

= {h}

), the correct formula is

$f'''(x_{i})=\;{f(x_{i+3})-8 f(x_{i+2})+13 f(x_{i+1})+13 f(x_{i-1})-8 f(x_{i-2})-f(x_{i-3})}/{8 h^{3}}$
$f'''(x_{i})=\;{-f(x_{i+3})-8 f(x_{i+2})-13 f(x_{i+1})+13 f(x_{i-1})+8 f(x_{i-2})-f(x_{i-3})}/{8 h^{3}}$
$f"'(x_{1})=\;{f(x_{1+3})-8 f(x_{i+2})-13 f(x_{i+1})+13 f(x_{i-1})+8 f(x_{1-2})+f(x_{i-3})}/{8 h^{3}}$
$f"'(x_{i})=\;{-f(x_{i+3})+8 f(x_{i+2})-13 f(x_{i+1})+13 f(x_{i-1})-8 f(x_{i-2})+f(x_{i-3})}/{8 h^{3}}$

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