Numerically integrate a time dependent differential equation
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Hi - I need to numerically integrate this equation: dCDF/dt=1/tr where tr = t0 * exp(bP/Tc). t0, b, and P are constants and Tc is defined as: Tc= {Te^4+K * [307.59-190.96 (ln〖t/24〗 )^0.24 ]}^(1/4) where Te, K are constants and t is changing between 1 to 300 days. The initial condition is CDF = 0 at t=ti. I want to integrate the dCDF/dt=1/tr in the forward time direction starting from t=ti until the CDF approach a finite value of 0.05. I appreciate your help.
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Torsten
il 1 Dic 2022
bP = 1;
Te = 1;
K = 1;
t0 = 1;
ti = 24;
CDF = @(x)integral(@(t) 1/t0*exp(-bP./(Te^4+K*(307.59-190.96*(log(t/24)).^0.24)).^0.25),ti,x)
x = ti:ti:300*ti;
F = arrayfun(@(x)CDF(x),x)
plot(x,F)
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Torsten
il 2 Dic 2022
@Alireza Mofidi comment moved here:
Yes, I understand. But what I'm looking for is to find out at which "t" the CDF will approach 0.05. I think my question was confusing.
Torsten
il 2 Dic 2022
As you can see, with the parameters I used for bP ,Te, K and t0, CDF tends to infinity as time grows. Insert the "correct" empirical parameters, run the code again and check the CDF curve shown. If it does not behave as you expect, recheck your model.
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