Help solving differential equations
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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
采纳的回答
Sam Chak
2022-5-7
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:
4 个评论
Juan Lara Alcaraz
2022-5-7
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
2022-5-7
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
2022-5-7
Sam Chak
2022-5-11
I hope that information in this link could help you. Always find a way...
更多回答（1 个）
Torsten
2022-5-6
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)
2 个评论
Juan Lara Alcaraz
2022-5-7
Torsten
2022-5-7
Yes. The equations are that easy that they can be solved using pencil and paper.
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