how to do iteration starting with a known number

hello i need to do an iteration process to obtain (pws) i have several variables that pws depend on and i need to know how to solve the problem here is a screenshot for the problem

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>> and all elements in the question are present like pts,tts,l and theta

thank you

[dpb]

What have you done so far?

[mohamed]

ok so far i got the first value but i dont know how to tell matlab to substitute with the new value of pws again

Answer 1

[Swastik Sarkar]

Hi Mohammed,

I believe this can be approached in two ways depending on whether you want to manually iterate or use MATLAB's Optimization Toolbox.

The Manual implementation of the iteration logic in MATLAB is like this:

pws1 = pts + 0.25 * (pts/100) * (L * cos(theta))/100;
currentIteration = 0;
maxIterations = 100 % Some limit as the solution might not converge
while currentIteration < maxIterations:
    Pavg = (pws1 + pts)/2; % pws1 is consumed here
    % do the other calculations
    % assign the new value of pws1
    pws1 = newlyCalculatedValue
    if(conditionMet):
        break
    end
end

Alternatively, if you're solving for pws such that it satisfies a fixed-point condition like pws = f(pws), you can use fsolve:

% Define the function to find the fixed point
f = @(pws) pws - someFunction(pws);  % Goal: pws = someFunction(pws)

pws1 = pts + 0.25 * (pts/100) * (L * cos(theta))/100;

% Solve using fsolve
options = optimoptions('fsolve', 'Display', 'iter');
[pws_solution, fval, exitflag] = fsolve(f, pws1, options);

This is more elegant if your iteration is actually trying to solve an equation implicitly.

For more information on fsolve, refer the following MathWorks Documentation:

https://www.mathworks.com/help/optim/ug/fsolve.html

Hope this helps converge to the solution.