How to set which variable to update in an iterative loop?

Hello, I have a couple of problems with my Matlab code. I have to set an iterative loop for the variable 'a_D1(z)'. 'a_D1(z)' is an input for a procedure that ends with a result, the one called 'c_x_av_D1(z)' in the code. But there is not an explicit function to relate them. Then I have another quantity, the one called 'c_x_av_mom_D1(z)', that can be explicitly expressed as a function of 'a_D1(z)'. Basically I have to iterate, updating the value of 'a_D1(z)', so that those 2 quantities are equal. Thank you.

a_D1(z)=0.1
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V_D1(z)=(1-a_D1(z))*V_0
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V_E1(z)=(1-2*a_D1(z))*V_0
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c_x_av_D1(z)=F_x_av_D1(z)/(1/2*rho*V_0^2*A_d(z))
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c_x_av1_D1(z)=4*a_D1(z)*(1-a_D1(z))

[James Tursa]

It is not clear to me. Are you trying to find values for which a system of equations will be equal? If so, what exactly do you what to be equal to what?

[Image Analyst]

What does "set an iterative loop" mean???

[Valerio Cittadini]

It is difficult to explain, I admit. Basically those c_x are the same quantity, but calculated with two different approaches, and that's why I called it in two different ways (c_x_av e c_x_av_mom). The first is calculated through a long procedure whose input is that 'a_D1', but there's no direct relation between them. The second can be calculated directly as a function of 'a_D1'. I have to find the value of 'a_D1' that makes the two equal.

[Valerio Cittadini]

Sorry, the two ways I called the quantity are c_x_av_D1 e c_x_av1_D1.

Answer 1

[Anh Tran]

HI Valerio,

My understanding is you just want to find a value of 'a_D1(z)' that makes 'c_x_av_D1' and 'c_x_av1_D1' have equal. You may use a 'while' loop which increases a_D1(z) by a small step size each iteration and terminates when the difference is equal to zero or less than a tolerance. 2 numbers can rarely be exactly equal because of floating-point representation accuracy, so I would suggest setting up a tolerance for their difference. You may need to change step_size and tolerance for your application (might result in an infinite loop if not set carefully along with your initial guess of a_D1). Good luck!

step_size = 0.0001;
tolerance = 0.001;
while terminate ~= 1
  a_D1(z) = a_D1(z) + step_size; % increment a_D1(z) with small step_size
  % calculate c_x_av_D1
  % calculate c_x_av1_D1
  if abs(c_x_av_D1 - c_x_av1_D1) < tolerance
      terminate = 1; % terminate the while loop
  end
end