The function $f\left(x\right)={e}^{x}-1$ is to be solved using Newton-Raphson method. If the initial value of x_{0} is taken as 1.0, then the absolute error observed at 2^{nd} iteration is _______.
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 x_{0}=1.2 is
Solution of the variables x_{1} and x_{2} 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 x_{1} = 0.0 and x_{2} = 1.0, the jacobian matrix is
Let x^{2} - 117 = 0 The iterative steps for the solution using Newton-Raphson's method is given by
Equation e^{x}-1=0 is required to be solved using Newton’s method with an initial guess x_{0}=-1.Then, after one step of Newton’s method, estimate x_{1} of the solution will be given by
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?