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I was trying to learn about solving integral equations using symbolic algorithms. After a quick web search, I mostly found items like this Mathematica journal article that mostly focuses on how to use Mathematica to get numerical solutions.

I am curious about whether computer algebra and more generally symbolic algorithms have been derived. What existing methods could be symbolically coded to get generic answers to non-linear integral equations.

Any links or references are appreciated.

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1 Answer

up vote 2 down vote accepted

What you are looking for is the topic typically called Computer Algebra.

For example:

Conferences

Group of Algebraic and Quantum Computations

Web Sites

Computer Algebra

Computer Algebra and Symbolic Computation: Elementary Algorithms

Symbolic Computation - also see the references.

Books

Algorithms for Computer Algebra Keith O. Geddes (Author), Stephen R. Czapor (Author), George Labahn (Author)

Computer Algebra and Symbolic Computation: Elementary Algorithms Joel S. Cohen (Author)

Modern Computer Algebra Joachim von zur Gathen (Author), Jürgen Gerhard (Author)

That should get you started to see if you can find your specific needs (there are various other books along these lines and some universities teach this topic and it is now typically considered a part Algebraic Geometry).

Lastly, you might find this useful too Introduction to Computer Algebra Systems

Regards -A

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Thanks Amzoti for your answer. I was aware of the term computer algebra (you could see that term actually in my question). What I was specifically looking for was references on computer algebra for the special topic of integral equations. I did not find any specific treatment of this in the references you mentioned. –  Learner Dec 16 '12 at 6:16
    
I recall that there was a book or notes on the topic, but cannot seem to locate it. You might have to peruse the books' TOC and see if you can find your specific topic and I know I have seen published papers on the topic. For example, search Berkeley and Symbolic Math and Integrals. For example sciencedirect.com/science/article/pii/S009630031000473X –  Amzoti Dec 16 '12 at 6:18
    
Thanks for that article. I will check it out. –  Learner Dec 16 '12 at 6:27
    
Another great "resource" post!! I'm guessing you have lots and lots of bookmarks on your browser(s)! –  amWhy May 14 '13 at 0:27
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