# Newton Raphson (NR) Method Algorithm (Step Wise)

## Newton Raphson Introduction

Newton Raphson Method is an open method and starts with one initial guess for finding real root of non-linear equations.

In Newton Raphson method if x0 is initial guess then next approximated root x1 is obtained by following formula:

```x1 = x0 - f(x0) / g(x0)
```

And an algorithm for Newton Raphson method involves repetition of above process i.e. we use x1 to find x2 and so on until we find the root within desired accuracy.

## Algorithm for Newton Raphson Method

An algorithm for Newton Raphson method requires following steps in order to solve any non-linear equation with the help of computational tools:

```1. Start

2. Define function as f(x)

3. Define first derivative of f(x) as g(x)

4. Input initial guess (x0), tolerable error (e)
and maximum iteration (N)

5. Initialize iteration counter i = 1

6. If g(x0) = 0 then print "Mathematical Error"
and goto (12) otherwise goto (7)

7. Calcualte x1 = x0 - f(x0) / g(x0)

8. Increment iteration counter i = i + 1

9. If i >= N then print "Not Convergent"
and goto (12) otherwise goto (10)

10. If |f(x1)| > e then set x0 = x1
and goto (6) otherwise goto (11)

11. Print root as x1

12. Stop
```