Help solve a system of Differential Equations

Hi everybody,

I have code to solve a system of Differential Equations with matrix. I do not know my mistakes. When I run my, error in my code " Undefined operator '*' for input arguments of type 'function_handle'.Error in osc (line 22) odes=diff(P)==(0.2*A+s*B)*P;"

Can you see it and help me fix it. Thanks so much!

----------------------------------------------

This is my code:

T=100; g=0.5*T; n=3;s0=0.5;lamda=0.2;
% khai bao ham xa xe (KNTH)
s=@(t)(s0).*(((t-floor(t/T)*T)<g))+(0)*(((t-floor(t/T)*T)>g));
t=linspace(0,500);
plot(t,s(t));
grid;
% Khai bao mt A vuong cap n+2
syms p1(t) p2(t) p3(t) p4(t) p5(t)
A=[-1 0 0 0 0;
    1 -1 0 0 0;
    0 1 -1 0 0;
    0 0 1 -1 0;
    0 0 0 1 0];
B=[0 1 0 0 0;
   0 -1 1 0 0;
   0 0 -1 1 0;
   0 0 0 -1 1;
   0 0 0 0 -1];
P=[p1; p2; p3; p4; p5];
odes=diff(P)==(0.2*A+s*B)*P;
[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes);
C=P(0)==[1;0;0;0;0];
[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes,C);

clf
fplot(p1Sol)
hold on
fplot(p2Sol)
hold on
fplot(p3Sol)
hold on
fplot(p4Sol)
hold on
fplot(p5Sol)
grid on
legend('p1Sol','p2Sol','p3Sol','p4Sol','p5Sol','Location','best')

-----------------------------------

[John D'Errico]

Since this is purely a numerical ODE solve, why are you using dsolve, instead of perhaps ODE45?

[Le Duc Long]

Hi John D'Errico,

Thanks for your anwser. I tried to solve with fix value of function s(t) with dsolve and it was ok. So i think maybe use dsolve. I think that the problem with my code at "odes=diff(P)==(0.2*A+s*B)*P;". Because s=s(t). How your opion about this?

syms p1(t) p2(t) p3(t) p4(t) p5(t)

A=[-1 0 0 0 0;

1 -1 0 0 0;

0 1 -1 0 0;

0 0 1 -1 0;

0 0 0 1 0];

B=[0 1 0 0 0;

0 -1 1 0 0;

0 0 -1 1 0;

0 0 0 -1 1;

0 0 0 0 -1];

P=[p1; p2; p3; p4; p5];

odes=diff(P)==(0.5*A+B)*P;

[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes);

C=P(0)==[1;0;0;0;0];

[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes,C);

clf

fplot(p1Sol)

hold on

fplot(p2Sol)

hold on

fplot(p3Sol)

hold on

fplot(p4Sol)

hold on

fplot(p5Sol)

grid on

legend('p1Sol','p2Sol','p3Sol','p4Sol','p5Sol','Location','best')

Answer 1

[Walter Roberson]

syms t
s = piecewise((t-floor(t/T)*T)<g,s0,0);
fplot(s, [0 500])
%do not do the numeric assignment to t

Note that you do did explicitly define s for the case where the expression exactly equals g, but the numeric logic you used would have come out as 0 for that case anyhow.

[Le Duc Long]

Thanks Walter Roberson,

Can you explain for me this error meaning?

% Tham so dau vao

T=100; g=0.5*T; n=3;s0=0.5;lamda=0.2;

% khai bao ham xa xe (KNTH)

syms t

s = piecewise((t-floor(t/T)*T)<g,s0,0);

fplot(s,[0 500]);

% Khai bao mt A vuong cap n+2

syms p1(t) p2(t) p3(t) p4(t) p5(t)

A=[-1 0 0 0 0;

1 -1 0 0 0;

0 1 -1 0 0;

0 0 1 -1 0;

0 0 0 1 0];

B=[0 1 0 0 0;

0 -1 1 0 0;

0 0 -1 1 0;

0 0 0 -1 1;

0 0 0 0 -1];

P=[p1; p2; p3; p4; p5];

odes=diff(P)==(0.2*A+s*B)*P;

[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes);

C=P(0)==[1;0;0;0;0];

[p1Sol(t),p2Sol(t),p3Sol(t),p4Sol(t),p5Sol(t)]=dsolve(odes,C);

clf

fplot(p1Sol)

hold on

fplot(p2Sol)

hold on

fplot(p3Sol)

hold on

fplot(p4Sol)

hold on

fplot(p5Sol)

grid on

legend('p1Sol','p2Sol','p3Sol','p4Sol','p5Sol','Location','best')