How to solve the parameters of a diffusion model?
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Qili Hu
el 13 de Abr. de 2023
Comentada: Walter Roberson
el 21 de Abr. de 2023
t= 0 5 10 15 20 30 45 60 75 90 105 120
qt= 0 3.87 4.62 4.98 5.21 5.40 5.45 5.50 5.51 5.52 5.54 5.53
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Alex Sha
el 21 de Abr. de 2023
Hi, Hu:
Step 1: finding the series root of qn (n=1,2,3...,) using fsolve or vpasolve one by one,alternatively, you may think other methods to quickly find solutions for different intervals together;
Step 2: based on the solutions from step 1, it is easy to use command, for example lsqcurvefit, to achieve the next fitting procedure.
The first 33 roots are given below, obtained very easy by using 1stOpt (a math package other than Matlab)
n=[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33];
qn=[4.35378367052701,7.48808641354398,10.5751624468592,13.6511427168261,16.7257079845738,19.8025583223684,22.8832678483399,25.9684490866884,29.0582237629463,32.1524537034099,35.2508675693218,38.3531340595364,41.4589045596711,44.5678374146667,47.6796109564883,50.7939296792504,53.9105263205883,57.0291615831204,60.1496225761141,63.2717206388126,66.3952889411584,69.520180089537,72.6462638614857,75.7734251293724,78.9015619953762,82.0305841384314,85.1604113617219,88.2909723238772,91.4222034345828,94.5540478954731,97.6864548680592,100.819378752091,103.952778559431];
You may then try the remain fitting process yourself.
Respuesta aceptada
Torsten
el 13 de Abr. de 2023
Editada: Torsten
el 13 de Abr. de 2023
- Make a code to determine the roots of your second equation.
- Make a code that evaluates the infinite sum to determine q_t from your first equation.
- Use MATLAB's "lsqcurvefit" to fit your parameters.
4 comentarios
Walter Roberson
el 21 de Abr. de 2023
We will not provide the code for you. However, we will assist you in correcting your attempt at the code once you have posted your attempted version.
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