How to write a code for iteration?

Hello. I'm new using Matlab. I have to programming the below diagram in Matlab. I think I'm doing well, so far. But I've got a doubt, that is how to write a code for iteration (the step in the third block)? I guess I have to use a 'while' but I didn't know how. Hope you can help me. I let what I've done so far, in case you need it in order to answer my question. I'm writing this code with the purpose of plotting a x-y diagram and a T-x-y diagram. Thanks.

    clear all; clc; close all
% Bubble temperature for P = 101.33 kPa
P = 101.33 %kPa
X = linspace (0,1,100)
phi = 1.0
x1 = X(1);        x2 = X(2);
% Wilson
    %PARAMETERS - System dependent
    a12 = 437.98; %cal/mol
    a21 = 1238.00; %cal/mol
    R = 1.9872; %cal/mol?K 
    V1 = 76.92; %cm3/mol 
    V2 = 18.07; %cm3/mol 
    comp = 2; 
    % Constants for Antoine equation for 2-propane(1), water(2)
    A1 = 16.6780;   B1 = 3640.20;   C1 = 53.54;
    A2 = 16.2887;   B2 = 3816.44;   C2 = 46.13;
    % Saturate temperature
    T1sat = (B1/(A1-(log(P)))-C1);
    T2sat = (B2/(A2-(log(P)))-C2);
    %Temperature
    T1 = sum(X*T1sat)
    T2 = sum(X*T2sat)
    % Activities
    A12 = (V2/V1)*exp(-a12/(R*T1)); 
    A21 = (V1/V2)*exp(-a21/(R*T2));
    % Vapour pressure
    P1sat = exp((A1-B1)/((T1)+C1));
    P2sat = exp((A2-B2)/((T2)+C2));
    for i=1:size(X,2)-1;
    x1 = X(i);        x2 = X(i+1);
    % Calc for Gammas
    ft1 = -log(x1 + 1-*A12);
    st1 = x2*((A12/(x1 + x2*A12))-(A21/(x2 + x1*A21)));
    gamma_1 = exp(ft1 + st1);
    ft2 = -log(x2 + x1*A21);
    st2 = x1*((A12/(x1 + x2*A12))-(A21/(x2 + x1*A21)));
    gamma_2 = exp(ft2 - st2);
    % j = Water
    % Vapour pressure (Pj), kPa
       Pjsat (i)= P/sum(((x2*gamma_2(i))/phi)*(P2sat/P2sat))
    % Temperature, K 
       Tj(i) = (A2/(B2 -(log(Pjsat (i))))-C2);
    % Vapour pressure, Pi_sat
       Pi_sat = exp((A2-B2)/((Tj(i))+C2));
    % Total pressure, P = 101.33 kPa
       Ptotal = P1sat*gamma_1(i)*x1 + P2sat*gamma_2(i)*x2;
       error = abs((101.33-Ptotal)/101.33);   
       counter = 0;  
       % Calc for y
          y (i) = ((x2*gamma_2(i)*Pi_sat)/phi*Ptotal);
       % Vapour pressure (Pj), kPa
          Pj_sat = P/sum(((x2*gamma_2(i))/phi)*(Pjsat/Pjsat))
       % Temperature, K
          Tj=(A2/(B2 -(log(Pj_sat)))-C2);
       % Iteration 
          if i>1
          while abs(Tj(i)-Tj(i-1))<1e-10
          break
          end
          else 
     end;

Answer 1

[Thorsten]

After the first box, you write

deltaT = epsilon + 1; % so that the while loop is entered
while deltaT >= epsilon

    % put code of the second box here

    deltaT = % add equation for new updated value of deltaT

 end

[Diyaa Khalifa]

Do you have codes for

Bulbble P calculations and Dew T calculations and Dew P calculations ??

Answer 2

[Rajesh]

Hello, i am using matlab code, please give anyone correct code.I attached fractal curve . The below curve and matlab program didnot match . please give correct code and shows different iterations.

clc; clear all; close all;

format 'short';

% Input data points

x = [0 3 4 5 6]; % x-coordinates

y = [3 6 1 7 5]; % y-coordinates

% Total points in the first iteration

%total_points = 17

% Number of original intervals

iter=3 %input('Enter the number of iterations:=');

N = length(x)

p=N

% % Compute the number of interpolated points per interval

% % Ensure total points = 17 (including original points)

% points_per_interval = floor((total_points - length(x)) / N);

% remaining_points = mod((total_points - length(x)), N);

% Spline parameters

alpha = [0.5 0.8 0.7 0.6]; % Scale control parameters

r = 3 * ones(1, N); % Recurrence or tension parameters

% Derivative values

d = [5.5 -3.5 0.5 2.0 -6.0];

d1 = [2 3 4 5 6];

% Prepare X1 and Y1 matrices for the initial interpolation data

X1 = zeros(4, 4); % Initialize X1 with zeros

x1 = [x(1) x(2) x(3) x(4)];

x2 = [x(2) x(3) x(4)];

x3 = [x(1) x(2) x(3)];

x4 = [x(2) x(3)];

t = [length(x1) length(x2) length(x3) length(x4)];

X1(1, 1:t(1)) = x1;

X1(2, 1:t(2)) = x2;

X1(3, 1:t(3)) = x3;

X1(4, 1:t(4)) = x4;

Y1 = zeros(4, 4); % Initialize Y1 with zeros

y1 = [y(1) y(2) y(3) y(4)];

y2 = [y(2) y(3) y(4)];

y3 = [y(1) y(2) y(3)];

y4 = [y(2) y(3)];

t = [length(y1) length(y2) length(y3) length(y4)];

Y1(1, 1:t(1)) = y1;

Y1(2, 1:t(2)) = y2;

Y1(3, 1:t(3)) = y3;

Y1(4, 1:t(4)) = y4;

% Initialize q, L, and L1 to avoid deletion error

q = zeros(1, 5) % Pre-allocate q to avoid the error

% Initialize storage for new points

X = []; % Interpolated x-coordinates

Y = []; % Interpolated y-coordinates

% Calculate a(i) and b(i) for each interval

for i = 1:N-1

a(i) = (x(i+1) - x(i)) / (X1(i, t(i)) - X1(i, 1));

b(i) = ((X1(i, t(i)) * x(i)) - (X1(i, 1) * x(i+1))) / (X1(i, t(i)) - X1(i, 1));

end

ab_values = [a' b']

T=((x(i) - X1(i, 1)) / (X1(i, t(i)) - X1(i, 1)))

for i = 1:N-1

% Calculate term1 using the formula provided

term1(i) = (y(i) - alpha(i) * Y1(i, 1)) * (1 -T ).^3

% Calculate term2 using the formula provided

term2(i) = [r(i) * (y(i) - alpha(i) * Y1(i, 1)) + (x(i+1) - x(i)) * d(i) - alpha(i) * ...

(d1(i) * (X1(i, t(i)) - X1(i, 1)))] * (1 - T).^2 *(T)

% Calculate term3 using the formula provided

term3(i) = [r(i) * (y(i+1) - alpha(i) * Y1(i, t(i))) - ((x(i+1) - x(i)) * d(i+1)) + alpha(i) * ...

(d1(i) * (X1(i, t(i)) - X1(i, 1)))] * (1 - T) * (T).^2

% Calculate term4 using the formula provided

term4(i) = (y(i+1) - alpha(i) * Y1(i, t(i))) * (T).^3

% Compute the numerator by summing all terms

numerator = term1(i) + term2(i) + term3(i) + term4(i)

% Compute the denominator

denominator = 1 + (r(i) - 3) * (1 - T)*(T)

% Calculate q(i) as the quotient of numerator and denominator

q(i) = numerator / denominator

end

L = []; L1 = []; X = []; Y = []; %X1=[]; Y1=[]; % Initialize matrices

% Perform iterations

for k = 1:iter

fprintf("ITERATION=%d\n", k);

for i = 1:N-1

for j = 1:t(i) % Use t(i) as the column bound

if k == 1 % First iteration

fprintf('(i,j) values (%d,%d)\n', i, j);

L(i, j) = a(i) * X1(i,j) + b(i);

L1(i, j) = alpha(i) * Y1(i,j) + q(i)*(X1(i,j));

else % More than one iteration

L(i, j) = a(i) * X1(i, j) + b(i);

L1(i, j) = alpha(i) * Y1(i,j) + q(i)*(X1(i,j));

end

end

% Store new points

X = [X, L(i, 1:t(i))]; % Append only valid columns

Y = [Y, L1(i, 1:t(i))]; % Append only valid columns

end

end

XX = [X, L(i, :)];

YY = [Y, L1(i, :)];

XX= unique (XX , 'rows') ;

X1=XX ( : , 1 ); Y1=XX ( : , 2 )

[X' Y']

% % Combine original points and interpolated points

X1 = unique([x, XX]) % Include original x-coordinates

Y1 = interp1(x, y, X1, 'linear'); % Ensure all x points map to a y value

% % Display Results

disp([X1', Y1'])

% % Plot Original and Interpolated Points

%subplot(ceil(iter/2), 2, k);

%plot(X1,Y1)

% Original points

plot(x, y, '.k', 'MarkerSize', 10); hold on;

% Interpolated curve

plot(X1, Y1, 'm-', 'LineWidth', 1.5);

xlabel('x');

ylabel('y');

title('Recurrent Rational Fractal Cubic Spline');

grid on;