How to solve the parameters of a diffusion model?

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Qili Hu 2023-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/1946298-how-to-solve-the-parameters-of-a-diffusion-model

评论： Walter Roberson 2023-4-21

采纳的回答： Torsten

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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Qili Hu 2023-4-20

Dear Sha

Thank you for your answer. I don't know how to write codes of this question. Can give me original MATLAB codes. Thank you very much.

Qili Hu

huqili@cdut.edu.cn

Alex Sha 2023-4-21

在 MATLAB Online 中打开

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.

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Torsten 2023-4-13

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https://ww2.mathworks.cn/matlabcentral/answers/1946298-how-to-solve-the-parameters-of-a-diffusion-model#answer_1215048

编辑：Torsten 2023-4-13

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.