Ode solver, how to pass V=0:0.1:1 used in the differential equations

The system of differential equations of the following format:

function dy=ff_corr(t,y)

dy=zeros(7,1);

E_B1 = 0.7; alpha_B1= 0.5; E_B2 = 0.8; alpha_B2 = 0.5; E_A1 = 0.2;alpha_A1 = 0.5; E_A2 = 0.6;

alpha_A2 = 0.5; E_A3 = 0.9; alpha_A3 = 0.5;E_C7 = 0.65; alpha_C7 = 0.5;k_rev = 0.3; T = 343.15;

F = 96487;R = 8.31434;r_ox = 0;theta = 1;b = (R.*T)./F;TauPt = 2.15; TauC = 4.6;

dy(1) =(F./TauPt).*(4.7e-5.*(y(3).*exp(alpha_B1.*(V-E_B1-r_ox.*theta)./b)-(k_rev.*y(1).*exp(-(1- alpha_B1).*(V-E_B1)./b)))-1.6e-1.*(y(1).*exp(alpha_B1.*(V-E_B2-r_ox.*theta)./b)-(k_rev.*y(2).*exp(-(1-alpha_B2).*(V-E_B2)./b)))-9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b));

dy(2) =(F./TauPt).*(1.5e-1.*(y(1).*exp(alpha_B1.*(V-E_B2-r_ox.*theta)./b)-(k_rev.*y(2).*exp(-(1-alpha_B2).*(V-E_B2)./b))));

dy(3) = (F./TauPt).*(9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b)-4.7e-5.*(y(3).*exp(alpha_B1.*(V-E_B1-r_ox.*theta)./b)-(k_rev.*y(1).*exp(-(1-alpha_B1).*(V-E_B1)./b))));

dy(4) =(F./TauC).*(1.62e-8.*((y(6).*exp(alpha_A1.*((V-E_A1)./b)))-(y(4).*exp(-(1-alpha_A1).*((V-E_A1)./b))))-6.7e-1.*((y(4).*exp(alpha_A2.*((V-E_A2)./b)))-(y(5).*exp(-(1-alpha_A2).*((V-E_A2)./b))))-1.17e-1.*y(4).*exp(alpha_A3.*((V-E_A3)./b))-9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b));

dy(5) =(F./TauC).*6.6e-1.*((y(4).*exp(alpha_A2.*((V-E_A2)./b)))-(y(5).*exp(-(1-alpha_A2).*((V-E_A2)./b))));

dy(6) =(F./TauC).*(9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b)-1.62e-8.*(y(6).*exp(alpha_A1.*(V-E_A1)./b))-(y(4).*exp(-(1-alpha_A1).*(V-E_A1)./b))+1.17e-1.*y(4).*exp(alpha_A3.*((V-E_A3)./b)));

dy(7) =-3.14e-14.*y(3).*(exp(0.5.*(V-1.188)./0.3)-(5e-5.*exp(-(1-0.5).*(V-1.188)./0.3)));

end

y0=[0;0;1;0;0;1;2e-9];

V=0:0.1:10;

[t, y] = ode45(@ff_corr,[0 10], y0);

[Sam Chak]

Hi @El Houssain Sabour

Does the system have an equilibrium when ? Just curious!

You forgot to supply the time vector for V. Is supposed to look like this? Something that adds "energy" into the system over time?

V = 0:0.1:10;
t = V;
plot(t, V, '.'), grid on, xlabel('t'), ylabel('V(t)')

Answer 1

[VBBV]

This is one way

clearvars
y0=[0;0;1;0;0;1;1];
V=0:0.1:1;
for k = 1:length(V)
    [t, y] = ode45(@(t,y) ff_corr(t,y,V(k)),[0 10], y0);
    plot(t,y(:,1))
    hold on
end

function dy=ff_corr(t,y,V)

dy=zeros(7,1);
E_B1 = 0.7; alpha_B1= 0.5; E_B2 = 0.8; alpha_B2 = 0.5; E_A1 = 0.2;alpha_A1 = 0.5; E_A2 = 0.6;                     
alpha_A2 = 0.5; E_A3 = 0.9; alpha_A3 = 0.5;E_C7 = 0.65; alpha_C7 = 0.5;k_rev = 0.3; T = 343.15;              
F = 96487;R = 8.31434;r_ox = 0;theta = 1;b = (R.*T)./F;TauPt = 2.15; TauC = 4.6;
dy(1)  =(F./TauPt).*(4.7e-5.*(y(3).*exp(alpha_B1.*(V-E_B1-r_ox.*theta)./b)-(k_rev.*y(1).*exp(-(1-alpha_B1).*(V-E_B1)./b)))-1.6e-1.*(y(1).*exp(alpha_B1.*(V-E_B2-r_ox.*theta)./b)-(k_rev.*y(2).*exp(-(1-alpha_B2).*(V-E_B2)./b)))-9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b));
dy(2)  =(F./TauPt).*(1.5e-1.*(y(1).*exp(alpha_B1.*(V-E_B2-r_ox.*theta)./b)-(k_rev.*y(2).*exp(-(1-alpha_B2).*(V-E_B2)./b))));
dy(3)  = (F./TauPt).*(9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b)-4.7e-5.*(y(3).*exp(alpha_B1.*(V-E_B1-r_ox.*theta)./b)-(k_rev.*y(1).*exp(-(1-alpha_B1).*(V-E_B1)./b))));
dy(4)  =(F./TauC).*(1.62e-8.*((y(6).*exp(alpha_A1.*((V-E_A1)./b)))-(y(4).*exp(-(1-alpha_A1).*((V-E_A1)./b))))-6.7e-1.*((y(4).*exp(alpha_A2.*((V-E_A2)./b)))-(y(5).*exp(-(1-alpha_A2).*((V-E_A2)./b))))-1.17e-1.*y(4).*exp(alpha_A3.*((V-E_A3)./b))-9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b));
dy(5)  =(F./TauC).*6.6e-1.*((y(4).*exp(alpha_A2.*((V-E_A2)./b)))-(y(5).*exp(-(1-alpha_A2).*((V-E_A2)./b))));
dy(6)  =(F./TauC).*(9.3e-3.*y(1).*y(4).*exp(alpha_C7.*(V-E_C7)./b)-1.62e-8.*(y(6).*exp(alpha_A1.*(V-E_A1)./b))-(y(4).*exp(-(1-alpha_A1).*(V-E_A1)./b))+1.17e-1.*y(4).*exp(alpha_A3.*((V-E_A3)./b)));
dy(7)  =-3.14e-14.*y(3).*(exp(0.5.*(V-1.188)./0.3)-(5e-5.*exp(-(1-0.5).*(V-1.188)./0.3)));
end

[El Houssain Sabour]

first of all thank you, unfortunately I got this error message.

Error using horzcat

Requested 6x178957200 (8.0GB) array exceeds maximum array size preference (8.0GB). This might cause MATLAB to become unresponsive.

Error in ode45 (line 476)

yout = [yout, zeros(neq,chunk,dataType)]; %#ok<AGROW>

Error in untitled4 (line 5)

[t, y] = ode45(@(t,y) ff_corr(t,y,V(k)),[0 10], y0);

Related documentation

[VBBV]

Its due to RAM limitations, You can try the suggestion given in this linkehttps://in.mathworks.com/matlabcentral/answers/844650-requested-48000x48000-17-2gb-array-exceeds-maximum-array-size-preference-creation-of-arrays-great#:~:text=Direct%20link%20to%20this%20answer,-https%3A%2F%2Fwww&text=1.,memory%20required%20by%20the%20data.

Answer 2

[Torsten]

So V should grow linearily from 0 to 10 in the differential equation ?

Then define it in @ff_corr as V = 10*t.