Optimization toolbox with ode45

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Alessia Nannetti 2021-3-15

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https://ww2.mathworks.cn/matlabcentral/answers/773717-optimization-toolbox-with-ode45

评论： Alan Weiss 2021-3-16

Thank you in advance for the help.

I want to use the optimization toolbox to find the correct value of v to get the condition that Y(end,2) = 0 instead of trying random v values in a for loop.

Does anyone has any suggestions in how can i do that?

here there is the code

v = [13:0.1:15]
for i=1:length(v)
    
u0 = (v(i)-ev-q*rd); %different values of pi_star at z=0 
%having varied Pac
f = @(z,y) [-(a*y(2))./((1-(y(1)./(b*xi_star))).^3);... %dpi_star_dz
  -y(1)/c]; %dq_star_dz
[z,Y] = ode45(f,[0 1],[u0 q_0]);
end 

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Answer 1

Alan Weiss 2021-3-15

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https://ww2.mathworks.cn/matlabcentral/answers/773717-optimization-toolbox-with-ode45#answer_648637

I guess that I would make a minimization problem for Y(end,2)^2. I don't know what your parameters are, but you can use fminbnd if you have a scalar parameter, or use lsqnonlin or one of the Global Optimization Toolbox solvers for multiple parameters.

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Alessia Nannetti 2021-3-15

the problem is that I want a specific value of v that returns me Y(end,2) = 0 (solution of the second equation of my sistem of odes).

v affects the value of u0 (which is one of my initial condition of the ode45).

I looked up your suggestions but my problem is that by knowing the minimum value (which is Y(end,2) = 0) find the correct value of v that affects the initial condition of my ode45 (u0)