Numerical Methods: 3 Point Formula

Click For Summary
SUMMARY

The discussion focuses on the application of the 3-point formula for approximating the first derivative of a function, specifically in a Numerical Methods course. The user encountered a challenge in estimating the derivative at the fourth point due to the lack of subsequent values. The conversation highlights that while the 3-point formula typically requires values from both sides of the point in question, an alternative approach using a negative step size (h) can be considered for the first point, suggesting a potential workaround for the fourth point.

PREREQUISITES
  • Understanding of Numerical Methods principles
  • Familiarity with derivative approximation techniques
  • Knowledge of 3-point formulas for derivative estimation
  • Basic calculus concepts, particularly limits and continuity
NEXT STEPS
  • Research the application of the 3-point formula in various contexts
  • Explore alternative numerical methods for derivative approximation
  • Learn about finite difference methods and their variations
  • Investigate the implications of using negative step sizes in numerical analysis
USEFUL FOR

Students in Numerical Methods courses, educators teaching calculus and numerical analysis, and professionals involved in computational mathematics or engineering applications.

bobmerhebi
Messages
38
Reaction score
0
Hello there,

I am taking a Numerical Methods course & i had a lecture today when we did an example on the 3-point formula to approximate the 1st derivative of f.

the example included 4 given x's with their images by f. & we had to get all the images for the 1st derivative of f.

so we used one of the two 3-point formulas to get the values for f' for each of the first 3 x's. the last x was left without an attempt to get its f'(x).

So tonight i was wondering about how could I apply the formula to get it & its seems that I can't, after all either of the 3 point formula's requires the values of either the previous & following x or the two values following x. In either cases that's not possible as there's is no value after this particular x.

my question is whether there's some kind of solution to this & if so or not how so ?

P.S. this is Not a HW question but rather a help in my lecture.

Thank you
 
Physics news on Phys.org
To estimate f' for the 4th point, can't you use the same method as the 1st point? In other words, can't h be negative?
 

Similar threads

MHB Calculate numerically the area
  • · Replies 8 ·
Replies
8
Views
2K
Mathematica Numerical integration over a Green's function
  • · Replies 13 ·
Replies
13
Views
3K
Numerical approximation of the 2nd derivative across a diffuse interface
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Finding a Rational Function with data (Pade approximation)
  • · Replies 4 ·
Replies
4
Views
2K
MATLAB Bisection method and numerical integration
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Numerical method to Lippman-Schwinger equation
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Proving Newton's forward difference interpolation formula
  • · Replies 1 ·
Replies
1
Views
1K
MHB Hayldiburasomas' question via email about Secant Method
  • · Replies 1 ·
Replies
1
Views
10K
Question about approximate numerical integration methods
  • · Replies 4 ·
Replies
4
Views
1K
Undergrad Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
  • · Replies 16 ·
Replies
16
Views
2K