1
GATE CE 2005
MCQ (Single Correct Answer)
+1
-0.3
Given $$a>0,$$ we wish to calculate it reciprocal value $${1 \over a}$$ by using Newton - Raphson method for $$f(x)=0.$$ The Newton - Raphson algorithm for the function will be
A
$${X_{k + 1}} = {1 \over 2}\left( {{X_k} + {a \over {{X_k}}}} \right)$$
B
$${X_{k + 1}} = {X_k} + {a \over 2}X_k^2$$
C
$${X_{k + 1}} = 2{X_k} - aX_k^2$$
D
$${X_{k + 1}} = 2{X_k} - {a \over 2}X_k^2$$
2
GATE CE 1995
Subjective
+1
-0
Let $$\,\,f\left( x \right) = x - \cos \,x.\,\,\,$$ Using Newton-Raphson method at the $$\,{\left( {n + 1} \right)^{th}}$$ iteration, the point $$\,{x_{n + 1}}$$ is computed from $${x_n}$$ as
3
GATE CE 1993
Fill in the Blanks
+1
-0
Given the differential equation $${y^1} = x - y$$ with initial condition $$y(0)=0.$$ The value of $$y(0.1)$$ calculated numerically upto the third place of decimal by the $${2^{nd}}$$ order Runge-Kutta method with step size $$h=0.1$$ is
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