1
GATE ECE 2016 Set 3
Numerical
+2
-0
Consider the first order initial value problem $$\,y' = y + 2x - {x^2},\,\,y\left( 0 \right) = 1,\,\left( {0 \le x < \infty } \right)$$ With exact solution $$y\left( x \right)\,\, = \,\,{x^2} + {e^x}.\,\,$$ For $$x=0.1,$$ the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size $$h=0.1$$ is __________.
2
GATE ECE 2014 Set 3
+2
-0.6
Match the application to appropriate numerical method

Applications
$$P1:$$ Numerical integration
$$P2:$$ Solution to a transcendental equation
$$P3:$$ Solution to a system of linear equations
$$P4:$$ Solution to a differential equation

Numerical Method
$$M1:$$ Newton-Raphson Method
$$M2:$$ Runge-Kutta Method
$$M3:$$ Simpson's $$1/3-$$rule
$$M4:$$ Gauss Elimination Method

A
$$P1 - M3,\,\,P2 - M2,\,\,P3 - M4,\,\,P4 - M1$$
B
$$P1 - M3,\,\,P2 - M1,\,\,P3 - M4,\,\,P4 - M2$$
C
$$P1 - M4,\,\,P2 - M1,\,\,P3 - M3,\,\,P4 - M2$$
D
$$P1 - M2,\,\,P2 - M1,\,\,P3 - M3,\,\,P4 - M4$$
3
GATE ECE 2005
+2
-0.6
Match the following and choose the correct combination

Group $$-$$ $${\rm I}$$
$$E.$$ Newton $$-$$ Raphson method
$$F.$$ Runge-Kutta method
$$G.$$ Simpson's Rule
$$H.$$ Gauss elimination

Group $$-$$ $${\rm II}$$
$$(1)$$ Solving non-linear equations
$$(2)$$ Solving linear simultaneous equations
$$(3)$$ Solving ordinary differential equations
$$(4)$$ Numerical integration method
$$(5)$$ Interpolation
$$(6)$$ Calculation of eigen values

A
$$E - 6,\,\,F - 1,\,\,G - 5,\,\,H - 3$$
B
$$E - 1,\,\,F - 6,\,\,G - 4,\,\,H - 3$$
C
$$E - 1,\,\,F - 3,\,\,G - 4,\,\,H - 2$$
D
$$E - 5,\,\,F - 3,\,\,G - 4,\,\,H - 1$$
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