Interpolation for numerical integration

Click For Summary
SUMMARY

The discussion centers on the best interpolation method for the function \(\Gamma(t)\) in the context of numerical integration, specifically within the integral \(\int\Gamma(t) * \tan (\Gamma(t)*t + \varphi)\). Participants suggest that Simpson's rule is a strong candidate for numerical integration methods. The inquiry also explores the potential of using approximations such as Taylor series or sine series to achieve analytical integration of the approximated expression.

PREREQUISITES
  • Understanding of numerical integration techniques, specifically Simpson's rule.
  • Familiarity with interpolation methods for functions defined at discrete points.
  • Knowledge of Taylor series and sine series for function approximation.
  • Basic concepts of integrals and their applications in mathematical analysis.
NEXT STEPS
  • Research the implementation and applications of Simpson's rule in numerical integration.
  • Explore various interpolation methods suitable for discrete functions.
  • Study Taylor series and sine series for approximating functions in integrals.
  • Investigate analytical integration techniques for approximated expressions.
USEFUL FOR

Mathematicians, numerical analysts, and engineers involved in numerical integration and function approximation will benefit from this discussion.

kaniello
Messages
21
Reaction score
0
Hallo,
[itex]\Gamma[/itex](t) is a function that i can know only at dicrete points and appears in this integral:
[itex]\int[/itex][itex]\Gamma[/itex](t) * tan ([itex]\Gamma(t)[/itex]*t + [itex]\varphi[/itex])
My question is now, which could be the best interpolation of [itex]\Gamma[/itex](t) that would allopw an exact integration?
Thank you very much in advance
 
Physics news on Phys.org
Simpon's rule is definitely a good option. What I was looking for is the following: imagine that in the place of [itex]\Gamma(t)[/itex] you have an approximation, like a Taylor series, or sine series or whatever, that would allow an analytical integration of this approximated expression.
 

Similar threads

Graduate Memory issues in numerical integration of oscillatory function
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Numerical Integration twice (acceleration to displacement)
  • · Replies 5 ·
Replies
5
Views
5K
Undergrad Find the value of this definite integral in terms of t, s and alpha
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Get equation that describes set of measured values
  • · Replies 16 ·
Replies
16
Views
2K
Graduate Error estimate for integral of interpolated function
  • · Replies 2 ·
Replies
2
Views
1K
Graduate How to take the spatial derivative of quaternions
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Did Math DF's integral calculator make a glaring mistake?
  • · Replies 8 ·
Replies
8
Views
4K
Graduate Multiplying divergent integrals using Hardy fields approach
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Conservation of Mass for Compressible Flow
  • · Replies 33 ·
2
Replies
33
Views
4K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
3K