List of top Engineering Mathematics Questions on Numerical Methods

The general solution of \[ \frac{dy}{dx} = \frac{1}{3x + 5y} \] is

The iterative formula to find the root of $ \sqrt[3]{x^2} = 2 $ using Newton-Raphson method is $ x_{n+1} = $

If $ A = [a_{ij}] $ is the coefficient matrix for a system of algebraic equations, then a sufficient condition for convergence of Gauss-Seidel iteration method is:

For applying Simpson's $ \frac{1}{3} $ rule, the given interval must be divided into how many number of sub-intervals?

Which of the following formula is used to fit a polynomial for interpolation with equally spaced data?

If $ A = [a_{ij}] $ is the coefficient matrix for a system of algebraic equations, then a sufficient condition for convergence of Gauss-Seidel iteration method is:

Cholesky decomposition is carried out on the following square matrix [A]. \[ [A] = \begin{bmatrix} 8 & -5 \\ -5 & a_{22} \end{bmatrix} \] Let $ l_{ij} $ and $ a_{ij} $ be the (i,j)\textsuperscript{th elements of matrices [L] and [A], respectively. If the element $ l_{22} $ of the decomposed lower triangular matrix [L] is 1.968, what is the value (rounded off to the nearest integer) of the element $ a_{22} $?}

If the values of $x$ are 1, 2, and 3 and the corresponding values of $y$ are 9, 8, and 10 respectively, then the slope of the line of regression equation of $y$ on $x$ is (up to 1 decimal place) __________________.

Using Simpson’s one-third rule (with step size $h=0.25$), the area under the curve $y = e^{-x^{3}}$, from $x=0$ to $x=1$ is ............. (rounded to two decimal places).

In the 4th order Runge-Kutta method for solving ordinary differential equations with step size $h<1$, the ratio of the order of local error to the order of global error is

Simpson’s one-third rule is used to estimate the definite integral $I=\displaystyle\int_{-1}^{1}\sqrt{1-x^{2}}\,dx$ with an interval length of $0.5$. Which one of the following is the CORRECT estimate of $I$ obtained using this rule?