From owner-help-octave at bevo dot che dot wisc dot edu  Thu Nov 30 20:28:09 1995
Subject: Re: can i do ODE2 problems with lsode ?
From: "H. I. SALEH" <salehh at peak dot org>
To: John Utz <spaz at u dot washington dot edu>
cc: help-octave at bevo dot che dot wisc dot edu
Date: Thu, 30 Nov 1995 18:22:13 -0800 (PST)



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.
> 
> *******************************************************************************
>  John Utz	spaz at u dot washington dot edu
> 	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