How to solve non linear system of ODE

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Ofek Aloush 2020-1-22

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回答： Star Strider 2020-1-22

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Hi all

I've searched all over MATLAB forums with no success. Please help!

I got these 3 ODE's:

The unkowns are:

Vc1, Vds, Vc3

All the rest of the variables are known.

I succeeded solving the first equation using the dsolve function.

I solved the second equation using solve to find V'c3 as a function of the other variables, then I've done dsolve for the expression I got, and equaled it to V'c3 in order to find Vc3 as a function of (time, Vds).

Now I'm trying to use ODE45 in order to find Vds from the 3rd equation, but I'm having trouble with it.

I got errors telling me to use numbers instead of variables, so I didn't add my code in here. I'm just afraid that it will be useless to you since it has number instead of variables (I used the numerical values of R1, R2, C3 Etc. instead of the variables themselves)

Let me know please if you think it's a good way of solving or if you have any other idea. I've tried everything! ????

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Answer 1

Star Strider 2020-1-22

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https://ww2.mathworks.cn/matlabcentral/answers/501540-how-to-solve-non-linear-system-of-ode#answer_411516

If you are fitting the differential equations to data, see Monod kinetics and curve fitting and Parameter Estimation for a System of Differential Equations for examples.

If you are starting with the Symbolic Math Toolbox, do not use dsolve to solve them if you want to estimate their parameters. Instead, do the procedure described in Matlab gives no result when I use the ODE (Ordinary Differential Equations) then use that ‘odefcn’ result as the differential equation to estimate the parameters.

Make appropriate changes so that your differential equations and data are compatible with the fitting or optimisation function you want to use.