How to function 𝑎𝐴 + 𝑏𝐵 → 𝑝P in ODE89

𝑎𝐴 + 𝑏𝐵 → 𝑝P

𝑑𝐴/𝑑𝑡 = −𝐾 ∗ 𝐴 ∗ 𝐵 𝑑𝐵/𝑑𝑡 = (𝑏/𝑎) ∗ (𝑑𝐴/𝑑𝑡) = −𝑌𝐵 ∗ (𝐾 ∗ 𝐴 ∗ 𝐵) 𝑑𝑃/𝑑𝑡 = −(𝑝/𝑎) ∗ (𝑑𝐴/𝑑𝑡) = 𝑌𝑃 ∗ (𝐾 ∗ 𝐴 ∗ 𝐵)

Answer 1

[Davide Masiello]

This should work:

clear,clc

tspan = [0,10];
y0    = [1,1,0];
[t,y] = ode89(@yourODEsystem,tspan,y0);

plot(t,y)
legend('A','B','P','Location','best')


function out = yourODEsystem(t,y)

% Coefficients
K = 1;
a = 2;
b = 1;
p = 0.5;

% Variables
A = y(1);
B = y(2);
P = y(3);

% Time derivatives
dAdt = -K*A*B;
dBdt = -(b/a)*K*A*B;
dPdt = (p/a)*K*A*B;

% Output
out = [dAdt;dBdt;dPdt];

end

Just replace you actual values of stoichiometric coefficients and kinetic constants.

[Torsten]

@Navaneetha Krishnan Murugadoss

Have in mind that chemical kinetics ODEs are usually stiff.

Use ode15s instead of ode89.

[Navaneetha Krishnan Murugadoss]

Error in TASK>odefcn (line 16)

A = y(1);

Error in TASK (line 6)

[t,y] = ode89(odefcn,tspan,y0);

[Davide Masiello]

Please show all your code. Moreover, please indicate what version of Matlab you are using.

[Navaneetha Krishnan Murugadoss]

clear,clc

tspan = [0,12];

y0=[0 1 3];

[t,y] = ode89(DEdef,tspan,y0);

plot(t,y)

legend('CL','NOM','DBP','Location','best')

function [Ddv_div] = odefcn(t,y)

% Coefficients

K = 5E-5;

YB=1;

YP=0.15;

% Variables

A = y(1);

B = y(2);

P = y(3);

% Time derivatives

dAdt = -K*A*B;

dBdt = -YB*(K*A*B);

dPdt = YP*(K*A*B);

Ddv_div = [-K*A*B;-YB*(K*A*B);YP*(K*A*B)];

% Output

out = [dAdt;dBdt;dPdt];

end

2021b version

[Navaneetha Krishnan Murugadoss]

I need to plot concentrations A,B, and P against time. I have to show how the concentrations change over time until ether A is completely depleted

[Davide Masiello]

The function call in ode89 must be equal to the function name. Write this

clear,clc
tspan = [0,12];
y0=[0 1 3];
[t,y] = ode89(@DEdef,tspan,y0);
plot(t,y)
legend('CL','NOM','DBP','Location','best')

function Ddv_div = DEdef(t,y)
% Coefficients
K = 5E-5;
YB=1;
YP=0.15;

% Variables
A = y(1);
B = y(2);
P = y(3);

% Output
Ddv_div = [-K*A*B;-YB*(K*A*B);YP*(K*A*B)];
end

However, let me point out that if the initial concentration of one of the two reactants is zero (like in your case) you won't observe any change in the concentration of any of the compounds, since the reaction cannot occur.