Solving series differential equation use ode45

i need to solve the following equations in matlab:

and my codes looks like this :

%initial condition

y0=[0;0;0];

%calling ode function

BO=[0.1 0.2 0.3 0.5 0.8 1 1.5 2];

for i=1:8

bo=BO(i);

[s,y]=ode45(@(s,y) lapalce(s,y,bo),[0 3],y0);

plot(s,y(1));

hold on

end

function dydt=lapalce(s,y,bo)

dydt=[2-bo*y(2)-((sin(y(1))/y(3)));

sin(y(1));

cos(y(1))];

end

matlab is giving me answers like

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

NaN NaN NaN

can anyone tell me what went wrong?

Answer 1

[Star Strider]

Yes!

The problem is:

y0=[0;0;0];

so:

sin(y(1))/y(3)

will be NaN because sin(0)=0, and 0/0 (and Inf/Inf) result in NaN values.

Settimg ‘y0’ to very small values instead:

y0=[0;0;0]+1E-12;

may give you useful output.

[Abert]

thank you, i am getting some results now, though it is different than what i thought to be. Need to check my equations.

[Star Strider]

As always, my pleasure!

Having all zero initial conditions (or initial estimates in other contexts and applications) is likely not the best approach.