Recent questions in Numerical Methods

Which one of the following options is correct for the given data in the table?$\begin{array}{|c|c|c|c|c|}\hline\text{Iteration (i)} & 0 & 1 & 2 & 3 \\ \hline\text{Input (...

Newton-Raphson method is used to compute the inverse of the number $1.6$. Among the following options, the initial guess of the solution that results in non-convergence o...

Consider a system given by the following first order differential equation:$$ \frac{d y}{d t}=y+2 t-t^{2} $$where, $y(0)=1$ and $0 \leq t<\infty$. Using a step size $h=0....

The Newton-Raphson method is applied to determine the solution of $f(x) = 0$ where $f(x) = x – \cos (x).$ If the initial guess of the solution is $x_{0} = 0,$ the value o...

The following table lists an $n^{th}$ order polynominal $f(x)=a_nx^n+a_{n-1}x^{n-1}+...+a_1x+a_0$ and the forward differences evaluated at equally spaced values of $x$. T...

The iteration step in order to solve for the cube roots of a given number N using the Newton-Raphson’s method is $x_{k+1}=x_k+\frac{1}{3}(N-x^3_k)$$x_{k+1}=\frac{1}{3}(2x...

While numerically solving the differential equation $\frac{dy}{dx}+2xy^2=0,\; y(0)=1$ using Euler’s predictor-corrector (improved Euler-Cauchy) method with a step size of...

Given $f(z)=\frac{1}{z+1}-\frac{2}{z+3}.$ If $C$ is a counterclockwise path in the $z$-plane such that $|z+1|=1,$ the value of $\frac{1}{2\pi j}\oint_cf(z)dz$ is$-2$$-1$$...

Consider the linear system x = $\begin{bmatrix}-1 & 0 \\0 & -2\end{bmatrix} x,$ with initial condition $x(0) = \begin{bmatrix}1 \\1\end{bmatrix}$. The solution $x(t)$ for...