## What is root in Newton-Raphson method?

The root of a function is the point at which f(x)=0. Many equations have more than one root. Every real polynomial of odd degree has an odd number of real roots (“Zero of a function,” 2016). Newton-Raphson is an iterative method that begins with an initial guess of the root.

**At which points the Newton Raphson method fails?**

Explanation: The points where the function f(x) approaches infinity are called as Stationary points. At stationary points Newton Raphson fails and hence it remains undefined for Stationary points.

### What is the starting value for Newton Raphson method?

How to Find the Initial Guess in Newton’s Method

- there is no best initial guess (that would be the root itself)
- instead, a suitable initial guess is needed.
- if quickly possible, plot the function.
- to compute a numerical approximation to a particular root, choose an initial guess close enough to that root.

**Does Newton Raphson converge?**

Newton Raphson Method is said to have quadratic convergence. Note: Alternatively, one can also prove the quadratic convergence of Newton-Raphson method based on the fixed – point theory. Any solution to (ii) is called a fixed point and it is a solution of (i).

#### What is the main drawback of NR method?

The main drawback of nr method is that its slow convergence rate and thousands of iterations may happen around critical point.

**Can Newton’s method be negative?**

To get started with Newton’s Method you need to select an initial value x_0. Newton’s Method works best if the starting value is close to the root you seeking. f(0) is also positive so any root must be negative. f(-1) is also positive but f(-2) is negative so there is a root between -1 and -2.

## What is 4th order Runge-Kutta method?

The Runge-Kutta method finds approximate value of y for a given x. Only first order ordinary differential equations can be solved by using the Runge Kutta 4th order method. Below is the formula used to compute next value yn+1 from previous value yn. The value of n are 0, 1, 2, 3, ….(x – x0)/h.