reduce-historical/r36/xlog/REACTEQN.LOG

REDUCE 3.6, 15-Jul-95, patched to 6 Mar 96 ...


% Examples for the conversion of reaction equations to ordinary
% differential equations.

% Example taken from Feinberg (Chemical Engineering):

   species := {A1,A2,A3,A4,A5};


species := {a1,

            a2,

            a3,

            a4,

            a5}


   reac2ode {  A1 + A4 <> 2A1,       rho, beta,
               A1 + A2 <> A3,        gamma, epsilon,
               A3      <> A2 + A5,   theta, mue};


                             2
{df(a1,t)=rho*a1*a4 - beta*a1  - gamma*a1*a2 + epsilon*a3,

 df(a2,t)= - gamma*a1*a2 + epsilon*a3 + theta*a3 - mue*a2*a5,

 df(a3,t)=gamma*a1*a2 - epsilon*a3 - theta*a3 + mue*a2*a5,

                                2
 df(a4,t)= - rho*a1*a4 + beta*a1 ,

 df(a5,t)=theta*a3 - mue*a2*a5}

        
  inputmat;


[1  0  0  1  0]
[             ]
[1  1  0  0  0]
[             ]
[0  0  1  0  0]



  outputmat;


[2  0  0  0  0]
[             ]
[0  0  1  0  0]
[             ]
[0  1  0  0  1]



% Computation of the classical reaction matrix as difference
% of output and input matrix:

  reactmat := outputmat-inputmat;


            [1   0   0   -1  0]
            [                 ]
reactmat := [-1  -1  1   0   0]
            [                 ]
            [0   1   -1  0   1]



% Example with automatic generation of rate constants and automatic
% extraction of species.
 
   species := {};


species := {}

   reac2ode {  A1 + A4 <> 2A1, 
               A1 + A2 <> A3,
               A3      <> A2 + A5};

new species: a1
new species: a4
new species: a2
new species: a3
new species: a5

               2
{df(a1,t)= - a1 *rate(2) + a1*a4*rate(1) - a1*a2*rate(3) + a3*rate(4),

            2
 df(a4,t)=a1 *rate(2) - a1*a4*rate(1),

 df(a2,t)= - a1*a2*rate(3) - a2*a5*rate(6) + a3*rate(5) + a3*rate(4),

 df(a3,t)=a1*a2*rate(3) + a2*a5*rate(6) - a3*rate(5) - a3*rate(4),

 df(a5,t)= - a2*a5*rate(6) + a3*rate(5)}

 
   on rounded;


   species := {};


species := {}

   reac2ode {  A1 + A4 <> 2A1, 17.3* 22.4**1.5,
                               0.04* 22.4**1.5 };

new species: a1
new species: a4

                             2
{df(a1,t)= - 4.24064598853*a1  + 1834.07939004*a1*a4,

                          2
 df(a4,t)=4.24064598853*a1  - 1834.07939004*a1*a4}


end;
(TIME:  reacteqn 110 130)