Numerically integrate a time dependent differential equation
2 Ansichten (letzte 30 Tage)
Ältere Kommentare anzeigen
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.
3 Kommentare
Antworten (1)
Torsten
am 1 Dez. 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)
4 Kommentare
Torsten
am 2 Dez. 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
am 2 Dez. 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.
Siehe auch
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!