% example of integrating two coupled ODE's with matlab
% A -> B -> C irreversible rxn in isothermal, isobaric PFR

% c holds the values of the dependent variables (concentrations)
% the first column of c holds the values of the concentration of A
% the second column of c holds the values of the concentration of B
% tau is the independent variable

% SPECIAL NOTE:  In many cases, your dependent variables will have different
% names.  For example, concentration of A and temperature.  In such a
% case, pick a general name such as "y" for the matrix that holds the dependent
% variables.  Then, the first column in y would hold the concentration
% values, and the second column of y would hold the temperature values.
% Write some comments defining the relationships and use these definitions in
% the main m-file and the m-file in which the derivatives are defined.

% declare "global" variables whose values are shared with file "deriv02.m"
global k1 k2
 
k1 = 1;       % rate constant of A -> B used in "deriv02.m"
k2 = 1;       % rate constant of B -> C used in "deriv02.m"

tauSpan = [0 10];  % set span of tau
c0 = [1; 0];  % set initial cond., cA = 1, cB = 0 at tau = 0

% call ode45 integrator
% 'deriv02' is defined in the file "deriv02.m"
% this is a user-written "m" file containing the
% derivative equations

[tau,c] = ode45('deriv02', tauSpan, c0);

% all the integration is finished now, so plot and save results

% pull individual cocentration columns out
cA = c(:,1);  % concentration of A
cB = c(:,2);  % concentration of B

plot(tau,cA,'b',tau,cB,'r')
title('example of integrating two ODEs')
xlabel('tau (space time)')
ylabel('concentration')
% put curve legends in color
% see "text" and "ColorSpec" in MATLAB manual
h = text(5,.6,'A');
set(h,'color','b')
h = text(5,.4,'B');
set(h,'color','r')

info = 'press any key to continue'
pause

% put tau and concentrations into one array
% so disk file will be in correct format for loading
% into graphing program

u = [tau, c];

info = 'Saving data tab-delimited text file "data02.temp"'
% col 1 = tau, col 2 = conc of A, col 3 = conc of B.
% IMPORT as Text file with Delimeter = Tab

save data02.temp u -ascii -tabs

info = '*** ex02 finished ***'