Thread Subject: dy/dt value from ode45 solver

Hi,

I just used ode45 to solve a set of differential equations and got value of my variables (say, y) plotted. How can I have the "dy/dt" value saved as well for each time step when I use ODE45 solver.

Actually, I am interested to find out the steady-state time using the above approach. I consider "dy/dt" as a slope for the y plot and would like to extract the time value for any given condition on Slope dy/dt.

Could you please suggest the way to save the dy/dt data value for ODE45 sovler?

Thanking you

Md. Shahriar Karim

On Aug 18, 3:58 pm, "Md. Shahriar Karim" <karim.shahr...@gmail.com>
wrote:
> Hi,
>
> I just used ode45 to solve a set of differential equations and got value of my variables (say, y) plotted. How can I have the "dy/dt" value saved as well for each time step when I use ODE45 solver.
>
> Actually, I am interested to find out the steady-state time using the above approach. I consider "dy/dt" as a slope for the y plot and would like to extract the time value for any given condition on Slope dy/dt.
>
> Could you please suggest the way to save the dy/dt data value for ODE45 sovler?
>
> Thanking you
>
> Md. Shahriar Karim

Hi,
One solution is to double the dimension of your system. write down the
eqns for d2y/dt2 also and append them to your state eqns.
ex:

if your original system is:

dy/dt = -y;

then d2y/dt2 = -dy/dt = y;

then your system is:

vdot = [-y; y];

return vdot

"Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
news:h6f14q$7a7$1@fred.mathworks.com...
> Hi,
>
> I just used ode45 to solve a set of differential equations and got value
> of my variables (say, y) plotted. How can I have the "dy/dt" value saved
> as well for each time step when I use ODE45 solver.

Call ODE45 and specify some output arguments (one if you want the SOL
solution struct array, two if you want t and y as individual vectors.) Then
plot the results (using DEVAL if you're using the SOL struct array.)

> Actually, I am interested to find out the steady-state time using the
> above approach. I consider "dy/dt" as a slope for the y plot and would
> like to extract the time value for any given condition on Slope dy/dt.

Write a function to DEVAL the SOL struct array at a given time and subtract
that result from the desired dy/dt, then use FZERO on that function.

--
Steve Lord
slord@mathworks.com

Hi Steve,

DEVAL asks for a structure input. I also replaced

[t, y]=ode45('steadystate', [0:0.1:10000], y0); part of my code by
sol=ode45('steadystate', [0:0.1:10000], y0);

but it didn't solve the problem. Again structure problem.

My code works as follows--

.......
y0(1)=70; y0(2)=0; y0(3)=200;y0(4)=0; y0(5)=0;
.......
.......
[t, y]=ode45('steadystate', [0:0.1:10000], y0); % I am calling another function "steadystate" %
or
% sol=ode45('steadystate', [0:0.1:10000], y0);

function dydt = steadystate(t,y)
......
B = y(1); C = y(2); D = y(3);E = y(4); M =y(5);
......
dydt(1)=... (differential Equation for B, C, D, E, M)
dydt(2)=...
.....
.....
dydt=dydt';

My target is to calculate the dy/dt value for variable "C"and once dy/dt value is available, I can put the checking condition for the slope calculation and find out my steady-state time accordingly.

Please suggest something again. Thanks,

Md. Shahriar Karim





"Steven Lord" <slord@mathworks.com> wrote in message <h6f5pa$hct$1@fred.mathworks.com>...
>
> "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
> news:h6f14q$7a7$1@fred.mathworks.com...
> > Hi,
> >
> > I just used ode45 to solve a set of differential equations and got value
> > of my variables (say, y) plotted. How can I have the "dy/dt" value saved
> > as well for each time step when I use ODE45 solver.
>
> Call ODE45 and specify some output arguments (one if you want the SOL
> solution struct array, two if you want t and y as individual vectors.) Then
> plot the results (using DEVAL if you're using the SOL struct array.)
>
> > Actually, I am interested to find out the steady-state time using the
> > above approach. I consider "dy/dt" as a slope for the y plot and would
> > like to extract the time value for any given condition on Slope dy/dt.
>
> Write a function to DEVAL the SOL struct array at a given time and subtract
> that result from the desired dy/dt, then use FZERO on that function.
>
> --
> Steve Lord
> slord@mathworks.com
>

"Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
news:h6fikv$egv$1@fred.mathworks.com...
> Hi Steve,
>
> DEVAL asks for a structure input. I also replaced
>
> [t, y]=ode45('steadystate', [0:0.1:10000], y0); part of my code by
> sol=ode45('steadystate', [0:0.1:10000], y0);

Try replacing the string input with a function handle to your function and
use the second of those syntaxes..

--
Steve Lord
slord@mathworks.com

Hi Steve,

Thanks for your help so far. However, I am totally unsure from the below part--

Write a function to DEVAL the SOL struct array at a given time and subtract
that result from the desired dy/dt, then use FZERO on that function.

 sol=ode45(@steadystate, [0:0.1:10000], y0);

once I do the above, I get my all variables value after solving the ODEs..variables are..B C D ..etc.

Now from this I am told to use the DEVAL on "sol", it gives me the values of my variables B,C,D...but I was needed the "dy/dt...the slope values.

Now, I am supposed to subtract my desired "dy/dt"..say 0.00001 from DEVAL output which is my variables values? Once this is done, I do FZERO on the result I get after subtraction....this is what I was told.

Could you please clarify how am I getting dy/dt out of the whole process? I am quite confused at this stage. Thanking you,

Md. Shahriar Karim



"Steven Lord" <slord@mathworks.com> wrote in message <h6firi$red$1@fred.mathworks.com>...
>
> "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
> news:h6fikv$egv$1@fred.mathworks.com...
> > Hi Steve,
> >
> > DEVAL asks for a structure input. I also replaced
> >
> > [t, y]=ode45('steadystate', [0:0.1:10000], y0); part of my code by
> > sol=ode45('steadystate', [0:0.1:10000], y0);
>
> Try replacing the string input with a function handle to your function and
> use the second of those syntaxes..
>
> --
> Steve Lord
> slord@mathworks.com
>

"Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message <h6h1q8$sp5$1@fred.mathworks.com>...
> Hi Steve,
>
> Thanks for your help so far. However, I am totally unsure from the below part--
>
> Write a function to DEVAL the SOL struct array at a given time and subtract
> that result from the desired dy/dt, then use FZERO on that function.
>
> sol=ode45(@steadystate, [0:0.1:10000], y0);
>
> once I do the above, I get my all variables value after solving the ODEs..variables are..B C D ..etc.
>
> Now from this I am told to use the DEVAL on "sol", it gives me the values of my variables B,C,D...but I was needed the "dy/dt...the slope values.
>
> Now, I am supposed to subtract my desired "dy/dt"..say 0.00001 from DEVAL output which is my variables values? Once this is done, I do FZERO on the result I get after subtraction....this is what I was told.
>
> Could you please clarify how am I getting dy/dt out of the whole process? I am quite confused at this stage. Thanking you,
>
> Md. Shahriar Karim
>
>
>
> "Steven Lord" <slord@mathworks.com> wrote in message <h6firi$red$1@fred.mathworks.com>...
> >
> > "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
> > news:h6fikv$egv$1@fred.mathworks.com...
> > > Hi Steve,
> > >
> > > DEVAL asks for a structure input. I also replaced
> > >
> > > [t, y]=ode45('steadystate', [0:0.1:10000], y0); part of my code by
> > > sol=ode45('steadystate', [0:0.1:10000], y0);
> >
> > Try replacing the string input with a function handle to your function and
> > use the second of those syntaxes..
> >
> > --
> > Steve Lord
> > slord@mathworks.com
> >

Actually, after you got the solution to the ODE, just call the function again you can get dy/dt, i.e.

[t, y]=ode45('steadystate', [0:0.1:10000], y0);
dydt = steadystate(t,y); %if your function is vectorized. Alternatively

dydt=y;
for k=1:numel(t)
 dydt(k,:)=steadystate(t(k),y(k,:));
end

HTH
Yi

Hi Cao,

Could you please explain the logic working here? Once I call the function again how does it give the dydt value?

is it that if I call the function again, it's going to give us the value of dy2dt2?

Thanks,

Md. Shahriar Karim


"Yi Cao" <y.cao@cranfield.ac.uk> wrote in message <h6hgs7$9uf$1@fred.mathworks.com>...
> "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message <h6h1q8$sp5$1@fred.mathworks.com>...
> > Hi Steve,
> >
> > Thanks for your help so far. However, I am totally unsure from the below part--
> >
> > Write a function to DEVAL the SOL struct array at a given time and subtract
> > that result from the desired dy/dt, then use FZERO on that function.
> >
> > sol=ode45(@steadystate, [0:0.1:10000], y0);
> >
> > once I do the above, I get my all variables value after solving the ODEs..variables are..B C D ..etc.
> >
> > Now from this I am told to use the DEVAL on "sol", it gives me the values of my variables B,C,D...but I was needed the "dy/dt...the slope values.
> >
> > Now, I am supposed to subtract my desired "dy/dt"..say 0.00001 from DEVAL output which is my variables values? Once this is done, I do FZERO on the result I get after subtraction....this is what I was told.
> >
> > Could you please clarify how am I getting dy/dt out of the whole process? I am quite confused at this stage. Thanking you,
> >
> > Md. Shahriar Karim
> >
> >
> >
> > "Steven Lord" <slord@mathworks.com> wrote in message <h6firi$red$1@fred.mathworks.com>...
> > >
> > > "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
> > > news:h6fikv$egv$1@fred.mathworks.com...
> > > > Hi Steve,
> > > >
> > > > DEVAL asks for a structure input. I also replaced
> > > >
> > > > [t, y]=ode45('steadystate', [0:0.1:10000], y0); part of my code by
> > > > sol=ode45('steadystate', [0:0.1:10000], y0);
> > >
> > > Try replacing the string input with a function handle to your function and
> > > use the second of those syntaxes..
> > >
> > > --
> > > Steve Lord
> > > slord@mathworks.com
> > >
>
> Actually, after you got the solution to the ODE, just call the function again you can get dy/dt, i.e.
>
> [t, y]=ode45('steadystate', [0:0.1:10000], y0);
> dydt = steadystate(t,y); %if your function is vectorized. Alternatively
>
> dydt=y;
> for k=1:numel(t)
> dydt(k,:)=steadystate(t(k),y(k,:));
> end
>
> HTH
> Yi

"Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
news:h6h1q8$sp5$1@fred.mathworks.com...
> Hi Steve,
>
> Thanks for your help so far. However, I am totally unsure from the below
> part--
>
> Write a function to DEVAL the SOL struct array at a given time and
> subtract
> that result from the desired dy/dt, then use FZERO on that function.
>
> sol=ode45(@steadystate, [0:0.1:10000], y0);
>
> once I do the above, I get my all variables value after solving the
> ODEs..variables are..B C D ..etc.
>
> Now from this I am told to use the DEVAL on "sol", it gives me the
> values of my variables B,C,D...but I was needed the "dy/dt...the slope
> values.
>
> Now, I am supposed to subtract my desired "dy/dt"..say 0.00001 from DEVAL
> output which is my variables values? Once this is done, I do FZERO on the
> result I get after subtraction....this is what I was told.
>
> Could you please clarify how am I getting dy/dt out of the whole process?
> I am quite confused at this stage. Thanking you,

After reading Yi's response, I think I misread your question and I _think_
it's simpler than I'm making it out to be, but I'm going to ask a
clarification question to make sure I understand what you're asking for.

    Are you trying to evaluate dy/dt at the times t and solution values y
returned by ODE45?

If so, just call your ODE function with those t and y inputs. Depending on
how you wrote your ODE function, you may need to loop over the elements of
the time vector and the rows of the solution vector. Remember, ODE45
requires a function that accepts t and y values and returns dy/dt evaluated
at those values -- which is precisely what I think you're looking for.

If that's not what you're looking for, please explain in a bit more depth
what you're trying to do.

--
Steve Lord
slord@mathworks.com

Hi Steve,

Thanks.

I need dy/dt value from a set of ODE. y value is not mandatory for me. however, it's okay if I have those. I have coded it in following manner--
***********************************************************
[t, y]=ode45('steadystate', [0:0.1:10000], y0);
% dydt=steadystate(t,y);
plot(t, y)
xlabel('TIME'); ylabel('Concentration of Species in Molecules');
dydt=y;
for k=1:numel(t)
    dydt(k,:)=steadystate(t(k),y(k,:));
end
save dydt;
slopeC=dydt(:,2);
for i=1:numel(t)
    if (slopeC(i)<0.000001)
        time=t(i)
        break;
    end
************************************************

But I am not yet clear how the calling of steadystate function is giving me the data dy/dt? Could you please explain a little bit?

Thanks,

Shahriar


"Steven Lord" <slord@mathworks.com> wrote in message <h6jv5k$mfq$1@fred.mathworks.com>...
>
> "Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
> news:h6h1q8$sp5$1@fred.mathworks.com...
> > Hi Steve,
> >
> > Thanks for your help so far. However, I am totally unsure from the below
> > part--
> >
> > Write a function to DEVAL the SOL struct array at a given time and
> > subtract
> > that result from the desired dy/dt, then use FZERO on that function.
> >
> > sol=ode45(@steadystate, [0:0.1:10000], y0);
> >
> > once I do the above, I get my all variables value after solving the
> > ODEs..variables are..B C D ..etc.
> >
> > Now from this I am told to use the DEVAL on "sol", it gives me the
> > values of my variables B,C,D...but I was needed the "dy/dt...the slope
> > values.
> >
> > Now, I am supposed to subtract my desired "dy/dt"..say 0.00001 from DEVAL
> > output which is my variables values? Once this is done, I do FZERO on the
> > result I get after subtraction....this is what I was told.
> >
> > Could you please clarify how am I getting dy/dt out of the whole process?
> > I am quite confused at this stage. Thanking you,
>
> After reading Yi's response, I think I misread your question and I _think_
> it's simpler than I'm making it out to be, but I'm going to ask a
> clarification question to make sure I understand what you're asking for.
>
> Are you trying to evaluate dy/dt at the times t and solution values y
> returned by ODE45?
>
> If so, just call your ODE function with those t and y inputs. Depending on
> how you wrote your ODE function, you may need to loop over the elements of
> the time vector and the rows of the solution vector. Remember, ODE45
> requires a function that accepts t and y values and returns dy/dt evaluated
> at those values -- which is precisely what I think you're looking for.
>
> If that's not what you're looking for, please explain in a bit more depth
> what you're trying to do.
>
> --
> Steve Lord
> slord@mathworks.com
>

"Md. Shahriar Karim" <karim.shahriar@gmail.com> wrote in message
news:h6k0q9$9f5$1@fred.mathworks.com...
> Hi Steve,
>
> Thanks.
>
> I need dy/dt value from a set of ODE. y value is not mandatory for me.
> however, it's okay if I have those. I have coded it in following manner--
> ***********************************************************
> [t, y]=ode45('steadystate', [0:0.1:10000], y0);
> % dydt=steadystate(t,y);
> plot(t, y)
> xlabel('TIME'); ylabel('Concentration of Species in Molecules');
> dydt=y;
> for k=1:numel(t)
> dydt(k,:)=steadystate(t(k),y(k,:));
> end

*snip*

> But I am not yet clear how the calling of steadystate function is giving
> me the data dy/dt? Could you please explain a little bit?

Remember, as stated in the documentation for ODE45, the first input argument
that it requires is a function that accepts two inputs, t and y, and returns
the right-hand side of the system of differential equations y' = dy/dt =
f(t, y). Thus the values from that function _are_ the dy/dt values you're
looking for.

--
Steve Lord
slord@mathworks.com