Optimization toolbox with ode45

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 

Answer 1

[Alan Weiss]

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.

[Alessia Nannetti]

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)

[Alan Weiss]

Maybe the question is "How can I connect an optimization solver and an ODE solver?" Here are some examples:

Fit ODE, Problem-Based

Fit an Ordinary Differential Equation (ODE)

Optimize an ODE in Parallel

It is possible that you would want to use fzero as the optimization solver.

Alan Weiss

MATLAB mathematical toolbox documentation