Solving Differential Equations using ODE45

Question

Zahra Ahmed 2019-11-9

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/490137-solving-differential-equations-using-ode45

评论： Star Strider 2019-11-9

Hello!

I am trying to find S from t= 0 to 10 but I couldn't manage to sort the code with the tutorials, S depends on X and I keep getting the error that I need an array of length 21 as an initial condition:

Equations:

ds/dt= D*(10-S)+rs

dx/dt= -D*X+um*X;

rs=-(ms*X+u*X/Y)

u=um*S/(k+S);

Code:

%Constants:

um=0.8; k=0.01; ms=0.05; Y=0.44; D=0.3; So=10;

t=0:0.5:10;

dxdt=@(t,X) -D*X+um*X;

[t,X]=ode45(dxdt, t, 1);

rs=-(ms*X+u*X/Y);

u=um*S/(k+S);

dsdt=@(t,S) D*(10-S)+rs;

[t,S]=ode45(dsdt, t, 10);

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Answer 1

Star Strider 2019-11-9

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/490137-solving-differential-equations-using-ode45#answer_400636

I decided to let the Symbolic Math Toolbox have a go at your equations, since they involved some substitutions:

syms S(t) X(t) um k ms Yc D So Y t 
u = um*S/(k+S);
rs = -(ms*X+u*X/Yc);
Eqns = [diff(S) == D*(10-S)+rs;  diff(X) == -D*X+um*X];
[VF,Sbs] = odeToVectorField(Eqns)
odefcn = matlabFunction( VF, 'Vars',{t,Y, um,k,ms,Yc,D})
um=0.8; k=0.01; ms=0.05; Yc=0.44; D=0.3; So=10;
tspan=0:0.5:10;
ic = [10, So];
[T,Y] = ode45(@(t,Y)odefcn(t,Y,um,k,ms,Yc,D), tspan, ic);
figure
plot(T, Y)
grid
legend(string(Sbs), 'Location','S')

I included the constants as arguments, rather than hard-coding them in your equations. I also assume that ‘So’ is the initial condition for ‘S(t)’. In this code, ‘S(t)’ is the second column of ‘Y’.