Integration
in [Matlab]
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From: Steven_Lord on 11 Aug 2010 09:59 "Roger Stafford" <ellieandrogerxyzzy(a)mindspring.com.invalid> wrote in message news:i3t093$mk5$1(a)fred.mathworks.com... > "Anna Kaladze" <anna.kaladze(a)gmail.com> wrote in message > <i3spl3$t1v$1(a)fred.mathworks.com>... >> Yes, thanks a lot for the answer and sorry, F(u) and f(u) are the SAME >> functions -- just a typo. Is there any code I can to write to solve the >> problem? I mean technically it is possible to solve the problem in Excel >> (one column for the inner integral where t argument will take the value >> from 0 to whatever), and then sum-up the values in that column using the >> trapezoidal rule. A smaller step size would give a reasoanble degree of >> approximation). But is there a way to do something like that in MATLAB? >> Thanks a lot. > - - - - - - - - - - - - > It's the statement "I have a non-integrable function, f(u)" that you made > in the first post that is the stumbling block here. In mathematics and in > matlab circles too, when you say a function is non-integrable, it is > because that function is sufficiently ill-behaved over the desired > integration range that it is impossible to obtain an integral for it. > Perhaps it ascends to infinity in the wrong way, the range is infinite and > it doesn't get small fast enough, or it is seriously discontinuous. An > example is the integral of 1/x^2*sin(1/x) from 0 to 2/pi which is not > well-behaved as it approaches x = 0. The integrated value keeps > oscillating endlessly back and forth more and more rapidly from -1 to +1 > as the lower limit approaches zero and consequently is non-integrable over > that full range. Now that I think about it a little more, there may still be hope, if the OP meant "I have a function that I can't symbolically integrate" when they said "non-integrable function f(u)". For example, if f(u) was exp(-u^2) and the OP didn't know about the error function ERF, it would appear this has no symbolic integral but it is possible to numerically evaluate the integral. > I am guessing since you are still talking about trying to get your > function's integral that this isn't what you meant by "non-integrable". > If so, you should take the advice you were given more seriously. The > double quadrature routine 'quad2d' allows for varying limits of > integration in its inner integral, which is what it sounds like you are > faced with when you say, "The inner integral (where integrand is F(u)) has > a low limit 0, but the upper limit is t (in principle, t takes the value > from 0 to 1)." I suggest you look into it. I second Roger's suggestion. -- Steve Lord slord(a)mathworks.com comp.soft-sys.matlab (CSSM) FAQ: http://matlabwiki.mathworks.com/MATLAB_FAQ To contact Technical Support use the Contact Us link on http://www.mathworks.com
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