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## Re: can i do ODE2 problems with lsode ?

 From: H. I. SALEH Subject: Re: can i do ODE2 problems with lsode ? Date: Thu, 30 Nov 1995 18:22:13 -0800 (PST)

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On Thu, 30 Nov 1995, John Utz wrote:

> Hi gang;
>
>       I have been trying to do some neural-net and dynamical systems
> stuff that i have been assigned as homework.
>
>       This means i need to solve ODE's and sytems of ODE's. Octave has
> dassl and lsode for this purpose. I am not sure how i need to pre process
> my equations to get them into a form that lsode or dassl would be willing
> to digest.
>
>       The example in the manual for lsode is pretty good, the entry for
> dassl does not have an example, but the description seems pretty complete.
>
>       Here is the function that i want to try and solve first, since i
> think it is a "simple" example of what comes in the real stuff.
>
>       d^2 x                       dx
>       ----- + lambda*( x^2 - 1 )* -- + x = 0
>         dt^2                        dt
>
> so we can plunk 3 in for lambda, this is supposedly an equation from a
> matlab demo, but i dont have matlab, so i dont know.
>
> my problem is that this is a 2nd order eq and lsode looks like it only
> wants 1rst order eq's.
>
>       Now, i *thought* that any nOrder ode can be represented as an
> Nsystem of 1rst order diffeq's. I starting to think that i hallucinated
> this fact because i cant seem to find any example of this in either
> Boyce/DiPrima or Jordan/Smith, which are the two textbooks on the subject
> of ode's that i have at my disposal.
>
>       So, did i hallucinate this? If not, can anybody provide any
> suggestions as to how i might implement this?
>
> tks folks, please feel free to tell me if u think this was an
> inapropriate use of the list.
>
> *******************************************************************************
>       idiocy is the impulse function in the convolution of life
>

Try the substitution y(t) = d x / dt. The above 2nd order ODE can be
written as the following 2 1st order ODEs

dx
----   = y(t)
dt

dy
----    + Lambda(x^2 - 1)y + x = 0
dt

I hope this helps.

H. I. SALEH

```