plot integral equation coming from ode solver

I have an equation that comes from ode solver :

[t1 V1] = ode15s(dV1dt, t1, y1); plot(t1, V1 ,'-b','lineWidth',2)

then I do some basic addition or subtraction on it for eg :

Aout1=(V1-1); plot(t1,Aout1,'-b','lineWidth',2);

Now I wish to integrate the output : So I tried with

final = integral (Aout1, 0, 4.2)

But I get error :

Error using integral (line 82) First input argument must be a function handle.  

I tried other things as well; but I don't achieve what I wish. Although 'cumsum' works well on it just like that.

Answer 1

[Star Strider]

Use the trapz (link) function:

idx = find(t1 <= 0.42);
final = trapz(t1(idx), Aout1(idx))

Since you menitoned cumsum, also see the documentation for cumtrapz (link).

[STP]

Hi Star Strider; I did read about it. Although if I just want to use to integral function; the error still is valid.

[Torsten]

The first argument to "integral" is a function handle, not a vector of values as in your case. So either use "trapz" or "cumtrapz" as suggested or include the integration in the call to ODE15S by defining a second equation dV2/dt = V1-1 besides dV1/dt =dV1dt.

[Star Strider]

@Torsten — Thank you.

[STP]

@torsten : I tried including integration in ode solver but still I didnt get it

dV1dt = @(t,V) ((U_in1*omega*beta)/Qo) - omega_half*V;

[t1 V1] = ode15s(dV1dt, t1, y1)

dV2dt = integral(V1-1);

[Amirah Algethami]

@Torsten How to extract the integration value is it :v2(:) or v2(end)???

This is your sugesstion :"include the integration in the call to ODE15S by defining a second equation dV2/dt = V1-1 besides dV1/dt =dV1dt"

[Torsten]

V2(i) = integral_{t=tspan(1)}^{t=tspan(i)} (V1(t)-1) dt (1 <= i <= end)

[Amirah Algethami]

thanks @Torsten this extract with defining dV2/dt = V1-1 , I thought ode15 will be integrated it without using integral function? please clarify it for me.

Thanks

[Torsten]

If you call ode15s with the additional ODE dV2/dt = V1(t)-1, V2(tspan(1)) = 0, ode15s will return

V2(i) = integral_{t=tspan(1)}^{t=tspan(i)} (V1(t)-1) dt (1 <= i <= end)

in the solution column for V2 in Y. The call somehow looks like

[T,Y] = ode15s(dVdt,tspan,[V1,0])

If you have further questions, please include executable code and mark the line where you have difficulties.