Help solving differential equations

Hello,

I need helping a differential equation using ode45().

I have the following statements and need to find tmax:

A(t) = dA/dt = -k0*A

A(0) = A0

B(t) = dB/dt = k0*A - k1*B

B(0) = 0

E(t) = dE/dt = k1*B

E(0) = 0

k0 = 0.01

k1 = 0.035

[Stephan]

Please provide the code you have so far.

[Juan Lara Alcaraz]

I was thinking of using a fuction like this function

dAdt = odefun(A,B,k0,k1)

dAdt = zeros(2,1);

dAdt = -k0*A;

dBdt = k0*A-k1*B;

dEdt=k1*B

end

It's all the code I have

Answer 1

[Sam Chak]

Hi @Juan Lara Alcaraz

Since you have written the code for the differential equations,

function dydt = odefcn(t, y)

dydt = zeros(3,1);

k0 = 0.01;

k1 = 0.035;

A = y(1);

B = y(2);

E = y(3);

dydt(1) = -k0*A;

dydt(2) = k0*A - k1*B;

dydt(3) = k1*B;

end

then you can use ode45 to obtain the numerical solution:

tspan = 0:0.1:1e3;      % simulation time
init = [1 0 0];         % assume initial values, A(0) = 1, B(0) = 1, E(0) = 0
[t, y] = ode45(@odefcn, tspan, init);

% For plotting purposes
% ---------------------
plot(t, y, 'linewidth', 1.5)
grid on
xlabel('Time, t [sec]')
title('Time responses of the System')
legend({'$A(t)$', '$B(t)$', '$E(t)$'}, 'Interpreter', 'latex', 'location', 'best')

Result:

[Juan Lara Alcaraz]

Thank you @Sam Chak. I don't understand why it isn't working, here I'll leave the screenshot of the error its giving me. Thank you again.

[Sam Chak]

Hey @Juan Lara Alcaraz

In one of your comments above, you have used odefcn() to define the system of differential equations.

But in your folder, you used myode. So, I guess this would solve the issue.

[t, y] = ode45(@myode, tspan, init);

Hope it helps.

[Juan Lara Alcaraz]

@Sam Chak Thank you so much!!!! IT WORKS!!

[Sam Chak]

Hi @Juan Lara Alcaraz

I hope that information in this link could help you. Always find a way...

https://www.mathworks.com/matlabcentral/answers/1685284-help-with-newton-raphson

Answer 2

[Torsten]

syms k0 k1 A0 A(t) B(t) E(t)
eqns = [diff(A,t)==-k0*A,diff(B,t)==k0*A-k1*B,diff(E,t)==k1*B];
conds = [A(0)==A0,B(0)==0,E(0)==0]
[Asol(t),Bsol(t),Esol(t)]=dsolve(eqns,conds)

[Juan Lara Alcaraz]

Is it possible to do it without extra toolboxes?

[Torsten]

Yes. The equations are that easy that they can be solved using pencil and paper.