1
GATE ECE 2010
+1
-0.3
Consider a differential equation $${{dy\left( x \right)} \over {dx}} - y\left( x \right) = x\,\,$$ with initial condition $$y(0)=0.$$ Using Euler's first order method with a step size of $$0.1$$ then the value of $$y$$ $$(0.3)$$ is
A
$$0.01$$
B
$$0.031$$
C
$$0.0631$$
D
$$0.1$$
2
GATE ECE 2008
+1
-0.3
The recursion relation to solve $$x = {e^{ - x}}$$ using Newton $$-$$ Raphson method is
A
$${x_{n + 1}} = {e^{ - {x_n}}}$$
B
$${x_{n + 1}} = {x_n} - {e^{ - {x_n}}}$$
C
$${x_{n + 1}} = {{\left( {1 + {x_n}} \right){e^{ - {x_n}}}} \over {\left( {1 + {e^{ - {x_n}}}} \right)}}$$
D
$${x_{n + 1}} = {{x_n^2 - {e^{ - {x_n}}}\left( {1 + {x_n}} \right) - 1} \over {{x_n} - {e^{ - {x_n}}}}}$$
3
GATE ECE 2007
+1
-0.3
The equation $${x^3} - {x^2} + 4x - 4 = 0\,\,$$ is to be solved using the Newton - Raphson method. If $$x=2$$ taken as the initial approximation of the solution then the next approximation using this method, will be
A
$$2/3$$
B
$$4/3$$
C
$$1$$
D
$$3/2$$
4
GATE ECE 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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