New algorithms for numerical integration and ODE solutions

03262014, 07:29 PM
Post: #8




RE: New algorithms for numerical integration and ODE solutions
(03132014 10:44 AM)Namir Wrote: I have posted on my web page two new algorithms for numerical integration Namir, Thank you for the articles. I have a question about your RombergSimpson Method. (I've seen it mentioned in passing that this could be done, but I've never actually seen it implemented.) Your algorithm uses: R(n,m) = (1/4^m1)*(4^m*R(n,m1)R(n1,m1))
for both the Trapezoid and Simpson methods. The derivation that I've seen for this recursive formula was based on the fact that the Trapezoid Error is proportional to 1/n^2. I'm not certain about this, but since the Simpson Error is proportional to 1/n^4, it seems like the recursive formula for Simpson's would be different. I could be totally wrong, but using a similar derivation, I'm coming up with: R(n,m) = (1/16^m1)*(16^m*R(n,m1)R(n1,m1))
I tried a couple of examples on a spreadsheet and this second formula seems to converge faster. Try it in your VB code and compare the two. Please correct me if I'm off on this. Wes L 

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