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Topic: Numerical Laplace transform
Replies: 0

 Vale Posts: 1 Registered: 9/9/13
Numerical Laplace transform
Posted: Sep 9, 2013 11:40 AM

Hi all!
I have a problem about computing numerically laplace transform from a vector.
I don't have the analytic form of the function that I would like to transform, because my data are a vector of values of concentration acquired at different time samples.

Ex:
time = [7.5;22.50262;37.50008;52.50036;67.50043;82.50053;97.50076;112.5008;127.501005;142.501;165.0011;195.0016;225.0018;255.002;285.0021;334.1693;394.1695;454.1707;514.171015;574.1711;685.1639;835.1641;1065.2923;1370.788;1675.5025;1980.81945;2285.738]./60;

Conc = [3.8;87.1;76.5;108.0;120.5;99.5;106.1;94.8;111.5;115.3;100.5;102.8;106.1;125.5;105.7;117.2;120.7;120.1;136.5;117.3;127.6;132.9;141.3;151.5;149.5;153.2;156.9];

I have tried to discretize the laplace transform using a trapezoidal rule as below:
N = length(time);
s = time;
Ns = length(s);

for j = 1 : Ns
a = cumtrapz( time, exp(-s(j).*time).*Conc);
L(j) = a(end) ;
end

but the numerical truncation error is significant (I have tried with a test function exp(-2t) and I have computed the analytic vs numerical transform computed as before and I have had two order of magnitude of difference).

How can I solve this problem? Do have any suggestion for a more accurate numerical integration?
Thank a lot
Vale