Need help with numerical integration

In summary, the best numerical method for integrating complicated integrands and singular functions is the use of Gauss quadratures, as suggested by many references. However, obtaining the abscissas and weights for a general function may be challenging, as it requires identifying the singularities in order to calculate the open-ended integrations of the sections between them. The book "Numerical Recipes for C" has a chapter on integration and provides information on the integration of improper integrals. A link to their website is available for more information.
  • #1
Rositta
13
0
Would anyone please suggest the best numerical method for integrating complicated integrands and singular functions? I find that Gauss quadratures are suggested by many references but I can't find a method to obtain the abscissas and weights for a general function.
 
Technology news on Phys.org
  • #2
Rositta said:
Would anyone please suggest the best numerical method for integrating complicated integrands and singular functions? I find that Gauss quadratures are suggested by many references but I can't find a method to obtain the abscissas and weights for a general function.

Welcome to PF, Rositta! :smile:

My book "Numerical Recipes for C" has a chapter on integration and in particular a paragraph on the integration of improper integrals.

As I understand it, you need to find out where the singularities are, so you can calculate open-ended integrations of the sections between the singularities.
 
  • #3
I like Serena said:
Welcome to PF, Rositta! :smile:

My book "Numerical Recipes for C" has a chapter on integration and in particular a paragraph on the integration of improper integrals.

As I understand it, you need to find out where the singularities are, so you can calculate open-ended integrations of the sections between the singularities.

Hi I like Serena :smile: Do you have a link to this? I am having no problem finding "Numerical Recipes in C" but not so much "for C" or is that what you meant?
 
  • #4
Saladsamurai said:
Hi I like Serena. Do you have a link to this? I am having no problem finding "Numerical Recipes in C" but not so much "for C" or is that what you meant?

Yep. That's what I meant.
Their website is here:
http://www.nr.com/
 
  • #5
Thaks all
 

1. What is numerical integration?

Numerical integration is a method used to approximate the value of a definite integral by dividing the area under a curve into smaller sections and using mathematical calculations to estimate the total area.

2. Why is numerical integration important?

Numerical integration is important because it allows us to calculate the value of integrals that cannot be solved analytically. It is also used in many scientific and engineering applications, such as in physics, economics, and statistics.

3. What are some common numerical integration methods?

Some common numerical integration methods include the trapezoidal rule, Simpson's rule, and Gaussian quadrature. Each method has its own advantages and is suitable for different types of integrals.

4. How accurate is numerical integration?

The accuracy of numerical integration depends on several factors, such as the method used, the number of intervals, and the complexity of the function. In general, the more intervals used, the more accurate the approximation will be.

5. Can numerical integration be used for all types of functions?

No, numerical integration is not suitable for all types of functions. It works best for smooth, continuous functions. Functions that are highly oscillatory or have discontinuities may require special methods or adjustments to achieve accurate results.

Similar threads

Replies
3
Views
336
  • Programming and Computer Science
Replies
5
Views
2K
  • Programming and Computer Science
Replies
6
Views
5K
  • Programming and Computer Science
Replies
15
Views
2K
Replies
2
Views
270
  • Calculus and Beyond Homework Help
Replies
4
Views
651
  • MATLAB, Maple, Mathematica, LaTeX
Replies
13
Views
2K
  • Quantum Physics
Replies
1
Views
538
  • Programming and Computer Science
Replies
1
Views
2K
Replies
1
Views
1K
Back
Top