New Quadratic Integration

05302018, 05:53 PM
(This post was last modified: 05302018 06:51 PM by Dieter.)
Post: #2




RE: New Quadratic Integration
(05302018 01:39 PM)Namir Wrote: I tested the above code with f(x)=x and f(x)=1/x and obtained good results. Namir, I have tried your code in VBA for Excel, and it seems to work fine. But for f(x)=1/x (your example) something happens that I do not understand. Let's assume a=1 and b=2 so that the true result is ln 2 = 0,693147180559945... n = 10 => 0,693146401483427 n = 20 => 0,693147131766058 n = 30 => 0,693147170917894 n = 40 => 0,705569697497420 (!!) n = 50 => 0,693147179310086 n = 60 => 0,701445982770560 (!!) n = 70 => 0,700264648002835 (!!) n = 80 => 0,699377730119543 (!!) n = 90 => 0,698687360816317 (!!) n=100 => 0,693147180481822 So the results first get more and more accurate as n increases, and the error is about 1/4 of a standard Simpson method. But then some results are way off. For instance for n=10 and n=16 the results are fine. For n=12 and n=14 they are off. Likewise n=20 and n=24 are fine, n=22 is not. What's going on here? Is there a special restriction for the value of n? You said it can be any positive value. EDIT: I think I found the problem. It's the exit condition of the loop. Due to roundoff errors the >= test does not test true if "a" is sliiiiightly less than "Blast". Testing floating point values for equality always is a bad idea. Instead you should check if the difference is below a certain threshold. But this is not required here: After replacing the DOloop with a FORloop everything works fine. I think you should adjust your program accordingly: Replace the DO line with FOR I=1 TO N Replace the LOOP UNTIL... line with NEXT I After this adjustment the program seems to work fine. For the example function the accuracy is comparable to a standard Simpson method with √2 n intervals. Dieter 

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Messages In This Thread 
New Quadratic Integration  Namir  05302018, 01:39 PM
RE: New Quadratic Integration  Dieter  05302018 05:53 PM
RE: New Quadratic Integration  Namir  05302018, 08:17 PM
RE: New Quadratic Integration  Dieter  05302018, 09:24 PM
RE: New Quadratic Integration  ttw  05312018, 02:27 AM
RE: New Quadratic Integration  Namir  05312018, 03:46 AM
RE: New Quadratic Integration  Namir  05312018, 03:51 AM
RE: New Quadratic Integration  ttw  05312018, 03:56 AM

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