## Code for Figure 5.11

### main.m

```
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92% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%
% This program is free software; you can redistribute it and/or
% modify it under the terms of the GNU General Public License as
% published by the Free Software Foundation; either version 2, or (at
% your option) any later version.
%
% This program is distributed in the hope that it will be useful, but
% WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
% General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; see the file COPYING.  If not, write to
% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
% MA 02111-1307, USA.

% This program "schm1_error.m" generates curves for the error in a
% series problem as the rate constant ratios for the first and
% second first-order reactions are varied.
% Last edited 1/30/97.
%
% Revised 7/24/2018

p = struct(); % Create structure to pass parameters to ode15s function
p.k1 = 1.0;

p.k2 = 1.0;
Initial = [1,0,0]';
t = [0:.01:1]';
opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);
answer = [t solution];

p.k2 = 10.0;
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);

p.k2 = 50.0;
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);

p.k2 = 1000.0;
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);

p.k2 = 10000.0;
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);

p.k2 = 100000.0;
[tsolver, solution] = ode15s(@(t,x) rxrate(t,x,p),t,Initial,opts);

% Strip out first row to avoid creating NaNs.

t_tmp = t(2:length(t));
c_Css = 1 - exp(-p.k1*t_tmp); %solution for k2 = Inf
answer2 = [t_tmp c_Css];

E = (c_Cexact - c_Css)./c_Cexact;
EE = abs(E);
error = log10(EE);
%answer3 = [t_tmp error];
% JBR, 2/22/98
answer3 = [t_tmp EE];

E = (c_Cexact - c_Css)./c_Cexact;
EE = abs(E);
error = log10(EE);
% JBR, 2/22/98

E = (c_Cexact - c_Css)./c_Cexact;
EE = abs(E);
error = log10(EE);
% JBR, 2/22/98

save -ascii schm1_error.dat answer3;

if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
% TITLE
end % PLOTTING

```

### rxrate.m

```
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9function dcdt = rxrate(t,x,p)
c1 = x(1);
c2 = x(2);
c3 = x(3);

r1 = p.k1*c1;
r2 = p.k2*c2;

dcdt = [-r1; r1-r2; r2];

```