Question

Newton-Raphson method is applicable to the solution of which equations?

Answer 1

Newton-Raphson method:

Newton-Raphson method is a way to find a good approximation for the root of a real valued function $f\left(x\right)$ and is applicable in transcendental equation.

Mostly it is used to find roots of nonlinear equation. This method uses the derivative of $f\left(x\right)atx$ to estimate a new value of the root.

The formula for the Newton-Raphson method is given as,

${\mathbf{x}}_{\mathbf{1}}\mathbf{=}{\mathbf{x}}_{\mathbf{0}}\mathbf{-}\frac{\mathbf{f}\left(x_0\right)}{{\mathbf{f}}^{\mathbf{\text{'}}}\left(x_0\right)}$

Where

• $f\left(x_0\right)=$ function at $x_0$
• $f^{\text{'}}\left(x_0\right)=$ first derivative of the function at $x_0$
• $x_0=$ Initial value

Hence, Newton-Raphson is applicable for transcendental equation.