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Could anyone suggest any good (perhaps online ref papers) reference material on numerical analysis focusing on determining accuracy/estimated errors, rates/orders of convergence especially when applied to ODEs? Thank you very much.

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    [Both](http://books.google.com/books?id=F93u7VcSRyYC) [of](http://books.google.com/books?id=m7c8nNLPwaIC) the books by Hairer and Wanner should be a good start.2011-08-21
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    I think this should be converted to community wiki.2011-08-21
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    I like [this book](http://books.google.com/books?id=YHXU4W3Ez2MC&printsec=frontcover&dq=numerical+methods&hl=en&ei=sIZRTo_cCM6N4gS6sNXEBw&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDcQ6AEwAzge#v=onepage&q&f=false). It has two chapters on ODEs.2011-08-21
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    I would insert "with practical advice" in between "chapters" and "on" in @joriki's comment.2011-08-21
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    @Dimitri: I disagree. As far as I know there aren't that many people here who could provide sound advice on numerical analysis, so I think it would be better to leave the question non-CW even if it might not have an objective correct answer. Reputation might serve as a little incitement to contribute a good answer.2011-08-22
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    @Theo, oh I'm sorry, I was just under the impression that these kind of questions should be converted to community wiki. However, you do provide a very reason why it shouldn't be converted.2011-08-22
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    @Dimitri: This is really just *my* opinion. I think many would disagree with that, but there is no consensus on CW questions that I'm aware of. Two meta discussions: http://meta.math.stackexchange.com/questions/2790/ and http://meta.math.stackexchange.com/questions/1700/2011-08-22
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    Thanks for the suggestions!2011-08-22

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