How to use 5 function coupled each other using ODE45? it is possible?

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cindyawati cindyawati
评论： cindyawati cindyawati 2023-6-20
I have a coupled differential equation. I'm confused why my M3, O, and P values are 0. Even though the initial conditions M2, M3, O and P are 0 but only M2 has a value. Is there something wrong with the function?
function CM1 = mymode (t,M1,M2,M3,O,P)
M1= 10;
M2 = 0;
M3 = 0;
O = 0;
P=0;
delta=50;
gamma=75;
K1= 10^-4;
K2=5*10^-4;
K3=10^-3;
Ko=0.1;
n=3;
Oa=10;
Pa=100;
mu_1=10^-3;
mu_2=10^-3;
mu_3=10^-3;
mu_o=10^-4;
mu_p= 10^-5;
CM1= zeros(5,1);
CM1(1) = (delta*M1*(1-(M1/gamma))-2*K1*M1*M1-M1*(K2*M2)-((Oa-n)*K3*M1*M3)-((Pa-Oa)*Ko*M1*O)-(mu_1*M1));
CM1(2) = (K1*M1*M1)-(K2*M1*M2)-(mu_2*M2);
CM1(3) = (K2*M1*M2)-(K3*M1*M3)-(mu_3*M3);
CM1(4) = (K3*M1*M3)-(Ko*M1*O)-(mu_o*O);
CM1(5) = (Ko*M1*O)-(mu_p*P);
end
[t,M1,M2,M3,O,P] = ode45(@mymode, [0,100],[0,0.01])
plot (t,M1,M2,M3,O,P)
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Torsten
Torsten 2023-6-20
编辑：Torsten 2023-6-20
Ran in:
This is a Runge-Kutta-4 code for your problem. Try to understand how "runge_kutta_RK4" works on your system of equations to do better next time.
tstart = 0.0;
tend = 100.0;
dt = 0.01;
T = (tstart:dt:tend).';
Y0 = [10 0 0 0 0];
f = @myode;
Y = runge_kutta_RK4(f,T,Y0);
M1 = Y(:,1);
M2 = Y(:,2);
M3 = Y(:,3);
O = Y(:,4);
P = Y(:,5);
figure
subplot(3,1,1)
plot(T,M1),grid, title('M1')
subplot(3,1,2)
plot(T,M2),grid, title('M2')
subplot(3,1,3)
plot(T,M3),grid, title('M3')
figure
subplot(2,1,1)
plot(T,O),grid, title('O')
subplot(2,1,2)
plot(T,P),grid, title('P')
function Y = runge_kutta_RK4(f,T,Y0)
N = numel(T);
n = numel(Y0);
Y = zeros(N,n);
Y(1,:) = Y0;
for i = 2:N
t = T(i-1);
y = Y(i-1,:);
h = T(i) - T(i-1);
k0 = f(t,y);
k1 = f(t+0.5*h,y+k0*0.5*h);
k2 = f(t+0.5*h,y+k1*0.5*h);
k3 = f(t+h,y+k2*h);
Y(i,:) = y + h/6*(k0+2*k1+2*k2+k3);
end
end
function CM1 = myode (~,MM)
M1 = MM(1);
M2 = MM(2);
M3 = MM(3);
O = MM(4);
P = MM(5);
delta=50;
gamma=75;
K1= 10^-4;
K2=5*10^-4;
K3=10^-3;
Ko=0.1;
n=3;
Oa=10;
Pa=100;
mu_1=10^-3;
mu_2=10^-3;
mu_3=10^-3;
mu_o=10^-4;
mu_p= 10^-5;
CM1= zeros(1,5);
CM1(1) = (delta*M1*(1-(M1/gamma))-2*K1*M1*M1-M1*(K2*M2)-((Oa-n)*K3*M1*M3)-((Pa-Oa)*Ko*M1*O)-(mu_1*M1));
CM1(2) = (K1*M1*M1)-(K2*M1*M2)-(mu_2*M2);
CM1(3) = (K2*M1*M2)-(K3*M1*M3)-(mu_3*M3);
CM1(4) = (K3*M1*M3)-(Ko*M1*O)-(mu_o*O);
CM1(5) = (Ko*M1*O)-(mu_p*P);
end

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采纳的回答

Alan Stevens
Alan Stevens 2023-6-20
Ran in:
Better like this:
MM0 = [10, 0, 0, 0, 0];
tspan = [0 100];
[t, MM] = ode15s(@mymode, tspan,MM0);
M1 = MM(:,1);
M2 = MM(:,2);
M3 = MM(:,3);
O = MM(:,4);
P = MM(:,5);
figure
subplot(3,1,1)
plot(t,M1),grid, title('M1')
subplot(3,1,2)
plot(t,M2),grid, title('M2')
subplot(3,1,3)
plot(t,M3),grid, title('M3')
figure
subplot(2,1,1)
plot(t,O),grid, title('O')
subplot(2,1,2)
plot(t,P),grid, title('P')
function CM1 = mymode (~,MM)
M1 = MM(1);
M2 = MM(2);
M3 = MM(3);
O = MM(4);
P = MM(5);
delta=50;
gamma=75;
K1= 10^-4;
K2=5*10^-4;
K3=10^-3;
Ko=0.1;
n=3;
Oa=10;
Pa=100;
mu_1=10^-3;
mu_2=10^-3;
mu_3=10^-3;
mu_o=10^-4;
mu_p= 10^-5;
CM1= zeros(5,1);
CM1(1) = (delta*M1*(1-(M1/gamma))-2*K1*M1*M1-M1*(K2*M2)-((Oa-n)*K3*M1*M3)-((Pa-Oa)*Ko*M1*O)-(mu_1*M1));
CM1(2) = (K1*M1*M1)-(K2*M1*M2)-(mu_2*M2);
CM1(3) = (K2*M1*M2)-(K3*M1*M3)-(mu_3*M3);
CM1(4) = (K3*M1*M3)-(Ko*M1*O)-(mu_o*O);
CM1(5) = (Ko*M1*O)-(mu_p*P);
end
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