Recent questions tagged numerical-methods

Match the following and choose the correct combination:$\begin{array}{ll} \textbf{Group 1} & \textbf{Group 2} \\ \text { E. Newton-Raphson method} & \text { 1. Solving no...

The equation $x^{3}-x^{2}+4 x-4=0$ is to be solved using the Newton-Raphson method. If $x=2$ is taken as the initial approximation of the solution, then the next approxim...

The recursion relation to solve $x=e^{-x}$ using Newton-Raphson method is$x_{n+1}=e^{-x_{n}}$$x_{n+1}=x_{n}-e^{-x_{n}}$$x_{n+1}=\left(1+x_{n}\right) \frac{e^{-x_{n}}}{1+e...

Simpson's rule for integration gives exact result when $f(x)$ is a polynomial of degree$1$$2$$3$$4$

Given the differential equation, $\bar{y}=x-y$ with the initial condition $y(0)=0$. The value of $(0.1)$ calculated numerically upto the third place of decimal by the sec...

A numerical solution of the equation $f(x)=x+\sqrt{x}-3=0$ can be obtained using Newton-Raphson method. If the starting value is $x=2$ for the iteration, the value of $x$...

Consider the first order initial value problem $$y’= y+2x-x^2 ,\ y(0)=1,\ (0 \leq x < \infty)$$ with exact solution $y(x) = x^2 + e^x$. For $x = 0.1$, the percentage dif...

The ROC (region of convergence) of the $z$-transform of a discrete-time signal is represented by the shaded region in the $z$-plane. If the signal $x[n]=(2.0)^{\mid n\mid...

Consider the sequence $x[n] = a^nu[n] + b^nu[n]$, where $u[n]$ denotes the unit-step sequence and $0<\mid a \mid < \mid b \mid<1$. The region of convergence (ROC) of the ...

The Newton-Raphson method is used to solve the equation $f(x) = x^{3} – 5x^{2} + 6x – 8 = 0.$ Taking the initial guess as $x = 5,$ the solution obtained at the end of the...

$\begin{Bmatrix} X_{n}\\ \end{Bmatrix}_{n=-\infty}^{n=\infty}$ is an independent and identically distributed (i.i.d.) random process with ܺ$X_{n}$ equally likely to be $+...

Match the application to appropriate numerical method.$\begin{array}{ll} \underline{\text{Application}} & \underline{\text{Numerical} \mid \text{Method}} \\ \text{P1: Nu...

Let $x[n] = \bigg( – \dfrac{1}{9}\bigg)^{n}u(n) \:– \bigg( – \dfrac{1}{3}\bigg)^{n}u(-n-1).$ The Region of Convergence (ROC) of the $z$-transform of $x[n]$is $\mid z \mid...

The maximum value of $\theta$ until which the approximation $\sin\theta \approx \theta $ holds to within $10\%$ error is$10^{\circ}$$18^{\circ}$$50^{\circ}$$90^{\circ}$

If $x[n]=(\frac{1}{3})^{|n|}-(\frac{1}{2})^{|n|}u[n]$, then the region of convergence (ROC) of its Z-transform in the Z-plane will be$\frac{1}{3}\lt |z|\lt 3$$\frac{1}{3}...

Starting with $x=1$, the solution of the equation $x^{3}+x=1$, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________.