Algorithm To Find Derivatives Using Newtons Backward Difference Formula

In this article, you will learn step by step procedure (algorithm) to find derivatives using Newton's backward interpolation formula.


Following steps are required inorder to find derivatives using backward difference formula:

1. Start

2. Read number of data (n)

3. Read data points for x and y:

    For i = 0 to n-1
        Read Xi and Yi,0
    Next i

4. Read calculation point where derivative is required (xp)

5. Set variable flag to 0

6. Check whether given point is valid data point or not.    
   If it is valid point then get its position at variable index
    For i = 0 to n-1
        If |xp - Xi| < 0.0001
            index = i
            flag = 1
            break from loop
        End If
    Next i 

7. If given calculation point (xp) is not in
   x-data then terminate the process.
    If flag = 0
        Print "Invalid Calculation Point"
    End If

8. Generate backward difference table
    For i = 1 to n-1
        For j = n-1 to i (Step -1)
            Yj,i = Yj,i-1 - Yj-1,i-1
        Next j
    Next i

9. Calculate finite difference: h = X1 - X0

10. Set sum = 0

11. Calculate sum of different terms in formula
    to find derivatives using Newton's backward 
    difference formula:
     For  i = 1 to index 
         term = (Yindex, i)i / i
         sum = sum + term
     Next i

12. Divide sum by finite difference (h) to get result
     first_derivative = sum/h

13. Display value of first_derivative

14. Stop