GATE Questions & Answers of Numerical Methods Electrical Engineering

The function fx=ex-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 _______.

When the Newton-Raphson method is applied to solve the equation f(x)=x3+2x-1=0,the solution at the end of the first iteration with the initial guess value as x0=1.2 is

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

equation (i) 10x2sinx1-0.8=0

equation (ii) 10x22-10x2cosx1-0.6=0

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

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

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

The differential equation dxdt=1-xτ is discretised using Euler’s numerical integration method with a time step ΔT>0. What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation?