Need help with numerical integration

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Discussion Overview

The discussion revolves around the best numerical methods for integrating complicated integrands and singular functions, with a focus on Gauss quadratures and the challenges of obtaining abscissas and weights for general functions. The context includes both theoretical and practical aspects of numerical integration.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • Some participants suggest that Gauss quadratures are commonly recommended for numerical integration but express difficulty in finding methods to obtain the necessary abscissas and weights for general functions.
  • One participant references a book, "Numerical Recipes for C," which includes a section on integrating improper integrals and emphasizes the importance of identifying singularities to perform open-ended integrations between them.
  • Another participant seeks clarification on the title of the referenced book, indicating confusion between "Numerical Recipes in C" and "Numerical Recipes for C."
  • A participant provides a link to the website for "Numerical Recipes," confirming the title they meant.

Areas of Agreement / Disagreement

Participants generally agree on the utility of Gauss quadratures for numerical integration but express differing levels of understanding and access to resources related to the methods for handling singular functions.

Contextual Notes

The discussion highlights potential limitations in accessing specific resources and the need for clarity on terminology related to numerical integration methods.

Rositta
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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.
 
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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.
 
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?
 
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/
 
Thaks all
 

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