Please explain this code about differential equations.

1 次查看（过去 30 天）
Mr.DDWW
Mr.DDWW 2022-5-7
回答： Sam Chak 2022-5-7
Here is the matlab code
theta=0.10895;
YF=0.0667;
alpha= 0.29;
beta= 0.68;
gamma1=450;
gamma2=11.25;
X0=0; Y0=0.0667; Z0=0;
f=@(t,y)[-y(1)/theta+(1+alpha)*gamma1*(1-y(1))*y(2)^2+beta*gamma1*(1-y(1))*y(3)^2;...
(YF-y(2))/theta+(1-alpha)*gamma1*(1-y(1))*y(2)^2-gamma2*y(2);...
-y(3)/theta+beta*gamma1*(1-y(1))*y(3)^2+2*alpha*gamma1*(1-y(1))*y(2)^2-gamma2*y(3)/beta];
[T,Y]=ode45(f,[100 120],[X0,Y0,Z0]);
plot(T,Y(:,1),'-',T,Y(:,3),'-.',T,Y(:,3),'.');
Can you please tell me where the underlined numbers (below) come from in f=@(t,y) ??????????
-y(1)
(1-y(1))*y(2)
(1-y(1))*y(3)^2
(YF-y(2))
(1-y(1))*y(2)^2-gamma2*y(2)
-y(3)/theta+beta
(1-y(1))*y(3)^2+2
y(2)^2-gamma2*y(3)/beta

请先登录，再回答此问题。

回答（2 个）

Star Strider
Star Strider 2022-5-7
They refer to the function values returned by ode45 (in this code).
y(1) is X
y(2) is Y
y(3) is Z
That can easily be inferred by comparing the code to the symbolic differential equation system.
Sam Chak
Sam Chak 2022-5-7
@Mr.DDWW
The code is annotated now. Hopefully sufficient for you to understand. By the way, I've fixed the plot line because you plotted Z(t) twice.
% Parameters
theta = 0.10895;
YF = 0.0667;
alpha = 0.29;
beta = 0.68;
gamma1 = 450;
gamma2 = 11.25;
% Initial values
X0 = 0;
Y0 = 0.0667;
Z0 = 0;
% A system of differential equations
f = @(t,y)[-y(1)/theta+(1+alpha)*gamma1*(1-y(1))*y(2)^2+beta*gamma1*(1-y(1))*y(3)^2;... % this is dX/dt
(YF-y(2))/theta+(1-alpha)*gamma1*(1-y(1))*y(2)^2-gamma2*y(2);... % this is dY/dt
-y(3)/theta+beta*gamma1*(1-y(1))*y(3)^2+2*alpha*gamma1*(1-y(1))*y(2)^2-gamma2*y(3)/beta]; % this is dZ/dt
% Solving the system f from time 100 s to 120 s with the initial values using the ode45 solver
[T, Y] = ode45(f, [100 120], [X0, Y0, Z0]);
% plotting the solutions for X(t), Y(t), Z(t)
plot(T, Y(:,1), '-', T, Y(:,2), '-.', T, Y(:,3), '.');
% additional stuff to display label, title, and legends
xlabel('Time, t [sec]')
title('Time responses of the System')
legend({'$X(t)$', '$Y(t)$', '$Z(t)$'}, 'Interpreter', 'latex', 'location', 'best')
Result:

类别

在 Help Center 和 File Exchange 中查找有关 Symbolic Math Toolbox 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by