1
GATE ME 2024
MCQ (Single Correct Answer)
+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
2
GATE ME 2022 Set 2
MCQ (Single Correct Answer)
+1
-0.33
Consider the definite integral
$\int^2_1(4x^2+2x+6)dx$
Let Ie be the exact value of the integral. If the same integral is estimated using Simpson’s rule with 10 equal subintervals, the value is Is. The percentage error is defined as e = 100 × (Ie - Is)/Ie The value of e is
3
GATE ME 2016 Set 3
MCQ (Single Correct Answer)
+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
4
GATE ME 2016 Set 2
MCQ (Single Correct Answer)
+1
-0.3
Numerical integration using trapezoidal rule gives the best result for a single variable function, which is
Questions Asked from Numerical Methods (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ME Subjects
Engineering Mechanics
Machine Design
Strength of Materials
Heat Transfer
Production Engineering
Industrial Engineering
Turbo Machinery
Theory of Machines
Engineering Mathematics
Fluid Mechanics
Thermodynamics
General Aptitude