1
GATE ME 2024
+1
-0.33

In order to numerically solve the ordinary differential equation dy/dt = -y for t > 0, with an initial condition y(0) = 1, the following scheme is employed:

$\frac{y_{n+1} - y_{n}}{\Delta t} = -\frac{1}{2}(y_{n+1} + y_{n}).$

Here, $\Delta t$ is the time step and $y_n = y(n\Delta t)$ for $n = 0, 1, 2, \ldots.$ This numerical scheme will yield a solution with non-physical oscillations for $\Delta t > h.$ The value of h is

A

$\frac{1}{2}$

B

$1$

C

$\frac{3}{2}$

D

$2$

2
GATE ME 2016 Set 3
+1
-0.3
The root of the function $$f\left( x \right) = {x^3} + x - 1$$ obtained after first iteration on application of Newton-Raphson scheme using an initial guess of $${x_0} = 1$$ is
A
$$0.682$$
B
$$0.686$$
C
$$0.750$$
D
$$1.000$$
3
GATE ME 2016 Set 2
+1
-0.3
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
A
linear
B
parabolic
C
logarithmic
D
hyperbolic
4
GATE ME 2014 Set 3
Numerical
+1
-0
The real root of the equation $$5x-2cosx=0$$ (up to two decimal accuracy) is