## Code for Figure 5.12

### main.m

```
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97% 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 "schm2_error.m" generates error curves for the
% reversible series problems as the reverse rate consant and
% the second rate constant are varied.  First-order reactions

% Last edited 1/30/97.

global k1 k_1 k2

k1 = 1;

Initial = [1,0,0]';
t = [0:.01:3]';
t_tmp = t(2:length(t));

k_1 = 100;
k2 = 100;

opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@rxrate,t,Initial,opts);
alpha = (k1*k2)/(k_1 + k2);
c_Css = 1-exp(-alpha*t_tmp);
c_Cexact = solution(2:end,3);
E=(c_Cexact - c_Css)./c_Cexact;
EE=abs(E);
error=log10(EE);
% JBR, 2/22/98

k_1 = 1;
k2 = 1000;

opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@rxrate,t,Initial,opts);
alpha = (k1*k2)/(k_1 + k2);
c_Css = 1-exp(-alpha*t_tmp);
c_Cexact = solution(2:end,3);
E=(c_Cexact - c_Css)./c_Cexact;
EE=abs(E);
error=log10(EE);
% JBR, 2/22/98

k_1 = 1000;
k2 = 1;

opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@rxrate,t,Initial,opts);
alpha = (k1*k2)/(k_1 + k2);
c_Css = 1-exp(-alpha*t_tmp);
c_Cexact = solution(2:end,3);
E=(c_Cexact - c_Css)./c_Cexact;
EE=abs(E);
error=log10(EE);
% JBR, 2/22/98
k_1 = 1000;
k2 = 1000;

opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, solution] = ode15s(@rxrate,t,Initial,opts);
alpha = (k1*k2)/(k_1 + k2);
c_Css = 1-exp(-alpha*t_tmp);
c_Cexact = solution(2:end,3);
E=(c_Cexact - c_Css)./c_Cexact;
EE=abs(E);
error=log10(EE);
% JBR, 2/22/98

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

```

### rxrate.m

```
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10function dcdt = rxrate(t,x)
global k1 k_1 k2
c1 = x(1);
c2 = x(2);
c3 = x(3);

r1 = k1*c1 - k_1*c2;
r2 = k2*c2;

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

```