1
GATE ECE 2017 Set 1
Numerical
+2
-0
Starting with $$x=1,$$ the solution of the equation $$\,{x^3} + x = 1,\,\,$$ after two iterations of Newton-Raphson's method (up to two decimal places) is ______________
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2
GATE ECE 2016 Set 2
Numerical
+2
-0
The ordinary differential equation $$\,\,{{dx} \over {dt}} = - 3x + 2,\,\,$$ with $$x(0)=1$$ is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is _________.
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3
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 __________.
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4
GATE ECE 2014 Set 3
MCQ (Single Correct Answer)
+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
$$P1 - M2,\,\,P2 - M1,\,\,P3 - M3,\,\,P4 - M4$$
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