MATLAB: Trying to code from Polymath

graphode45polymath

Im supposed to turn this Polymath code into a Matlab code but Im not sure how. Please help. Its supposed to use an ode solver and a graph

Best Answer

Here's a basic MATLAB version. 
% Initial conditions
Ca0 = 2;
Cb0 = 4;
Cc0 = 0;
Cd0 = 0;
T0  = 800;
IC = [Ca0 Cb0 Cc0 Cd0 T0];
% V range
Vspan = [0 10];
% Call ode solver
[V, CT] = ode45(@fn, Vspan, IC);
% Extract parameters

 Ca = CT(:,1);
 Cb = CT(:,2);
 Cc = CT(:,3);
 Cd = CT(:,4);
 T  = CT(:,5);
 
 % Plot graphs
 figure
 plot(V,Ca,V,Cb,V,Cc,V,Cd),grid
 xlabel('V'),ylabel('Ca.Cb.Cc,Cd')
 legend('Ca','Cb','Cc','Cd')
 
 figure
 plot(V,T),grid
 xlabel('V'),ylabel('T')
% ODE function
function dCTdV = fn(~,CT)
        % Data
        Cpa = 20;
        dh1a = 20000;
        dh2a = -10000;
        vo = 10;
        % Extract parameters
         Ca = CT(1);
         Cb = CT(2);
         Cc = CT(3);
         Cd = CT(4);
         T  = CT(5);
         
        % k and r functions
        k1a = 0.001*exp(-5000/1.987*(1/T - 1/300));
        k2a = 0.001*exp(-7500/1.987*(1/T - 1/300));
        r1a = -k1a*Ca*Cb^2;
        r2a = -k2a*Ca*Cc;
         % odes
         dCTdV = [(r1a+r2a)/vo;
                   2*r1a/vo;
                   (-2*r1a+r2a)/vo;
                   -2*r2a/vo;
                   (r1a*dh1a + r2a*dh2a)/((Ca+Cb+3*Cc+4*Cd)*vo*Cpa)];
 
end
I'll leave you to construct the tabular form of the results.
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