Consider the first order initial value problem
${y}^{\text{'}}=y+2x-{x}^{2},y\left(0\right)=1,\left(0\le x<\infty \right)$
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 first iteration is _____.
Match the application to appropriate numerical method.
A polynomial $f(x)={a}_{4}{x}^{4}+{a}_{3}{x}^{3}+{a}_{2}{x}^{2}+{a}_{1}x-{a}_{0}$ 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:
The equation x^{3} - x^{2} + 4x - 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 approximation using this method will be