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Numerical first derivative using different methods

3 December, 2020 Leave a comment Go to comments

I numerically computed the first derivative of the following function at interior points using different methods, in an uniform grid of points. Also, I found the average of the absolute error of the predicted first derivative for all the interior points, providing the best prediction.

f(x)=sin[(4-x)(4+x)], 0 <= x <= 8
Numerical methods used:

  • Piecewise quadratic spline functions that represent the function
  • 1st order forward scheme
  • 2nd central difference
  • Padé approximation

Plot of results for each approach along with the exact solution.

Numerical Derivative - Laura Almara. Numerical Derivative Errors by Almara

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