# GATE Questions & Answers of Numerical Methods Electrical Engineering

#### Numerical Methods 6 Question(s)

The function $f\left(x\right)={e}^{x}-1$ is to be solved using Newton-Raphson method. If the initial value of x0 is taken as 1.0, then the absolute error observed at 2nd iteration is _______.

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When the Newton-Raphson method is applied to solve the equation $f\left(x\right)={x}^{3}+2x-1=0$,the solution at the end of the first iteration with the initial guess value as x0=1.2 is

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Solution of the variables x1 and x2 for the following equations is to be obtained by employing the Newton-Raphson iterative method.

equation (i) $10{x}_{2}\mathrm{sin}{x}_{1}-0.8=0$

equation (ii) $10{x}_{2}^{2}-10{x}_{2}\mathrm{cos}{x}_{1}-0.6=0$

Assuming the initial valued x1 = 0.0 and x2 = 1.0, the jacobian matrix is

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Let x2 - 117 = 0 The iterative steps for the solution using Newton-Raphson's method is given by

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Equation ex-1=0 is required to be solved using Newton’s method with an initial guess x0=-1.Then, after one step of Newton’s method, estimate x1  of the solution will be given by

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The differential equation $\frac{dx}{dt}=\frac{1-x}{\tau }$ is discretised using Euler’s numerical integration method with a time step $\Delta T>0$. What is the maximum permissible value of $\Delta T$ to ensure stability of the solution of the corresponding discrete time equation?