Thread Subject:

How to use ODE 15s to solve this equation.

Could someone please elaborate on how to use ODE 15s or 45 for this differential equation?

(1/beta) *(d alpha/dT) = ln A*(1-alpha)- (E/RT)

I have the value of alpha and E as a function of a.

I need to generate graph of alpha Vs Temperature and d alpha/dT versus Temperature.

On 6/24/2012 7:59 PM, Sriraam wrote:
> Could someone please elaborate on how to use ODE 15s or 45 for this differential equation?
>
> (1/beta) *(d alpha/dT) = ln A*(1-alpha)- (E/RT)
>
> I have the value of alpha and E as a function of a.
>
> I need to generate graph of alpha Vs Temperature and d alpha/dT versus Temperature.
>

Just like you would do with any ode.

Need to write you differential equation in the form
    
          y' = f(t,y)

The function f(t,y) is what is called the "ode function". The
thing you put as first argument to ode45 call, as in

     [t,y]=ode45(@f,[t0 tfinal],initial_conditions);

so, it is your job to first express your ode system in the
the form y'=f(t,y). Matlab will not do that part for you. Need
paper and pencil for that. Even if your original ode was not
first order, need to convert everything to first order
ode's.

once you do that, then you can code it. In the above, y is
called the dependent variable, and 't' is the independent
variable.

see help for many examples.

--Nasser

"Nasser M. Abbasi" <nma@12000.org> wrote in message <js8eh4$6et$1@speranza.aioe.org>...
> On 6/24/2012 7:59 PM, Sriraam wrote:
> > Could someone please elaborate on how to use ODE 15s or 45 for this differential equation?
> >
> > (1/beta) *(d alpha/dT) = ln A*(1-alpha)- (E/RT)
> >
> > I have the value of alpha and E as a function of a.
> >
> > I need to generate graph of alpha Vs Temperature and d alpha/dT versus Temperature.
> >
>
> Just like you would do with any ode.
>
> Need to write you differential equation in the form
>
> y' = f(t,y)
>
> The function f(t,y) is what is called the "ode function". The
> thing you put as first argument to ode45 call, as in
>
> [t,y]=ode45(@f,[t0 tfinal],initial_conditions);
>
> so, it is your job to first express your ode system in the
> the form y'=f(t,y). Matlab will not do that part for you. Need
> paper and pencil for that. Even if your original ode was not
> first order, need to convert everything to first order
> ode's.
>
> once you do that, then you can code it. In the above, y is
> called the dependent variable, and 't' is the independent
> variable.
>
> see help for many examples.
>
> --Nasser

Thank you for your suggestion. I am sorry, I am really a beginner in MATLAB while I understand the ODE.
My ode will be d(alpha)/dt = A exp (-E/R*T))(1-alpha). ie y'=f(y,T) and T=To+beta*t

Here is when it gets complicated. I need the alpha values with respect to temperature. So A and E I can provide as input at each alpha.

"Sriraam" wrote in message <js8d4r$o6f$1@newscl01ah.mathworks.com>...
> Could someone please elaborate on how to use ODE 15s or 45 for this differential equation?
>
> (1/beta) *(d alpha/dT) = ln A*(1-alpha)- (E/RT)
>
> I have the value of alpha and E as a function of a.
>
> I need to generate graph of alpha Vs Temperature and d alpha/dT versus Temperature.

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It might help (no promises) if you stated the expressions of alpha and E as functions of a. Are they also functions of T, and is 'a' = 'A' or is it a different function or variable?