Hi Sean. I uploaded the new version of code (replaced original code). Now it is calculating finite difference table fd but still some problem in Do Loop where I have two different criteria to update matrix "fd". I am expecting logic in IF which is supposed to work for all element in row (nas1+1) as I start updating matrix from right. However logic is failing after second iteration. Hence matrix is getting incorrectly updated from (10,4)th element. (10,4)th element is computed using previous value of (11,5)th matrix fd (which is 1).Can you opine why Do loop is not updating in correct sequence?

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It looks like you need to debug your code.

Debugging code is easier when the code has been broking up into smaller parts. Each smaller part can be tested and checked to make sure it works correctly.

1. What kinds of error messages do you see? Maybe pick one at a time.
2. What part of your code does the error message refer to?

If looks like you've set the variable nas to be a string, but later on you use it as a number.

The Wolfram Language uses square brackets for calling a function. So you should write:

boptval["100", "1", "20", "5", "c", "100", "80"]

Also, boptval is defined to take 8 arguments. Here you have given it 7 arguments.