List of top Mechanical Engineering Questions on Numerical Methods asked in CUET (PG)

Using Runge-Kutta method of fourth order, an approximate value of \(y\) at \(x=0.2\), given that \(\frac{dy}{dx}=\frac{y^2-x^2}{y^2+x^2}\) and \(y(0)=1\), is:

Using the method of Regula Falsi, a root of the equation \( x^3 + x^2 - 3x - 3 = 0 \) lying between 1 and 2 is

The value of the integral
\[ \int_{0.2}^{1.4} (\sin x - \log_e x + e^x) \, dx \]
using Simpson's three-eighth rule, by taking interval size \( h = 0.2 \), is: