# GATE Questions & Answers of Numerical Methods Electronics and Communication Engg

#### Numerical Methods 9 Question(s)

Starting with x=1, the solution of the equation x3+x=1, after two iterations of Newton-Raphson’s method (up to two decimal places) is__________

Consider the first order initial value problem

${y}^{\text{'}}=y+2x-{x}^{2},y\left(0\right)=1,\left(0\le x<\infty \right)$

with exact solution $y\left(x\right)=x^2+e^x.$ For $x=0.1,$ the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with step-size $h = 0.1$ is __________

The Newton-Raphson method is used to solve the equation f(x) = x3 – 5x2 + 6x – 8 = 0. Taking the initial guess as x = 5, the solution obtained at the end of the first iteration is _____.

Match the application to appropriate numerical method.

 Application Numerical |Method P1: Numerical integration M1: Newton-Raphson Method P2: Solution to a transcendental equation M2: Runge-Kutta Method P3: Solution to a system of linear equations M3: Simpson’s 1/3-rule P4: Solution to a differential equation M4: Gauss Elimination Method

A polynomial $f\left(x\right)={a}_{4}{x}^{4}+{a}_{3}{x}^{3}+{a}_{2}{x}^{2}+{a}_{1}x-{a}_{0}$ with all coefficients positive has

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

The recursion relation to solve x=e-x using Newton Raphson method is

For the function ${e}^{-x}$, the linear approximation around x = 2 is: