What is Numerical differentiation: Definition and 11 Discussions

In numerical analysis, numerical differentiation describes algorithms for estimating the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function.

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  1. T

    Numerical Differentiation: Comparing Central & Other Formulas

    Hello there, I have found a different central differentiation formula for a first derivate from what I am used to seeing and I was wondering if they were the same one. I am struggling to find the Numerical Differentiation formulas (forward, backward and central) in scholarly articles and I have...
  2. R

    I Smoothing Numerical Differentiation Noise

    I am using the "knife-edge" technique to find the intensity profile of a rectangular laser beam. The data that is obtained using this method is power, the integral of intensity. Therefore, to get the intensity profile we must differentiate the data. So, as expected, my data looks like a ramp...
  3. O

    Python Wave on string: How can I create a traveling triangle pulse?

    I have the following program that moves a wave on a string with fixed ends. The program solves the wave equation given a initial condition wave. The initial condition is a triangle wave splitting into two pulses. Here is the code written in Python: from numpy import * from matplotlib.pyplot...
  4. R

    MATLAB How Accurate is Numerical Differentiation of sin(x) at 0.4?

    I am trying to estimate the second derivative of ##sin(x)## at ##0.4## for ##h=10^{-k}, \ \ k=1, 2, ..., 20## using: $$\frac{f(x+h)-2f(x)+f(x-h)}{h^2}, \ \ (1)$$ I know the exact value has to be ##f''(0.4)=-sin(0.4)= -0.389418342308651.## I also want to plot the error as a function ##h## in...
  5. K

    MHB Intermediate Value Thm for Five-Point Formula

    I have a specific, for-learning-sake-only question on how the author of this link: http://www.math.ucla.edu/~yanovsky/Teaching/Math151A/hw5/Hw5_solutions.pdf gets past the details of the Intermediate Value Theorem on the following paragraph. If someone could fill in the details for me, it...
  6. Z

    MHB Complex Step Numerical Differentiation

    Well I think this is really cool, numerical differentiation of real analytic functions by stepping out of the reals: Complex Step Differentiation | Cleve's Corner Even funnier is John D'errico's comment (my amusement is mainly due to the idea that a fourth order finite differences scheme with...
  7. D

    Numerical differentiation with change of variable

    Hi all I am trying to solve for an integral whose integrand is a derivative that has a change of variable inside of it. ∫ (dz/dx) * cos(θ) dθ between 0 and pi. I have a function for z(x), and also know the relation between of x and θ, but what I don't know is how to evaluate such...
  8. E

    Numerical differentiation of a dataset

    I have a dataset in two columns X and Y, sorted in ascending values of X. I'm trying to find its numerical derivative, however, the "noise" (it's very hard to see any noise in the dataset itself when plotted), but the noise gets massively amplified to the point where the numerical derivative...
  9. M

    Implicit numerical differentiation

    Homework Statement I am using Crank–Nicolson to solve a logistic function, modeling population growth. To get the next time step, I have to solve a quadratic equation. The problem is that i get two solutions for y(i+1). Does it mean that I am doing it wrong? If not, can I just pick the...
  10. P

    Numerical differentiation using forward, backward and central finite difference

    ive been given this question for a uni assignment: given the function: f (x) = 5(x^1.3) +1.5(7x − 3)+ 3(e^− x) + ln(2.5(x^3)) find the first derivative at all possible points within the interval [0, 6], with step length h = 1 for: forward difference aproximation, backward difference...
  11. D

    Numerical Differentiation: Difference approximation on numerical data

    Homework Statement I am given a table of data derived from experiment. A force (F) is applied to a spring and the extension (x) is measured and recorded. An additional column of data for the derivative (dF/dx) is also provided. Here is the data: x(m) F(kN) df/dx (kN/m) 0.0...