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From: pradeep on 24 Feb 2007 02:21

Hi all
i have this rather innocuous looking NDSolve command thats crashing the
mathematica kernel,
NDSolve[{y'[x]==Min[s[x]+Sin[x],Cos[x]-s[x]],y[0]==0,s[x]==x^2},{y,s},{x,0,3}]

If i were to substitute s[x] in this equation with x^2 and then try
solving, i get an answer, if i assign s[x] in advance and try solving
it, i still get an answer but the nature of the algorithm followed by
NDSolve doesnt allow it to take s[x] as a dependent variable and still
have it occur inside the Min function! i find that weird!
Someone have an explanation??
thanks in advance!
Pradeep
p.s. also note the that the nature of my application is such that i'd
like to solve this bunch of equations in a single shot without
assignment statements hence i dont have use for the two approaches that
i mentioned worked.

From: Jens-Peer Kuska on 28 Feb 2007 04:24
Hi,

have you ever taken a look onto the conditions,
that a numerical solution of an initial value
problem exists ??

There is a propery of the right hand side
called Lipshitz continuous and Min[] will
violate this condition.

Second, you don't need assigment statements
because


NDSolve[
{y'[x]==Min[s[x]+Sin[x],Cos[x]-s[x]],y[0]==0}/.
s[x]->x^2,
y,{x,0,3}]

will work
and instead of s[x]->x^2
you may use the output of Solve[]

Regards
Jens

pradeep wrote:
> Hi all
> i have this rather innocuous looking NDSolve command thats crashing the
> mathematica kernel,
> NDSolve[{y'[x]==Min[s[x]+Sin[x],Cos[x]-s[x]],y[0]==0,s[x]==x^2},{y,s},{x,0,3}]
>
> If i were to substitute s[x] in this equation with x^2 and then try
> solving, i get an answer, if i assign s[x] in advance and try solving
> it, i still get an answer but the nature of the algorithm followed by
> NDSolve doesnt allow it to take s[x] as a dependent variable and still
> have it occur inside the Min function! i find that weird!
> Someone have an explanation??
> thanks in advance!
> Pradeep
> p.s. also note the that the nature of my application is such that i'd
> like to solve this bunch of equations in a single shot without
> assignment statements hence i dont have use for the two approaches that
> i mentioned worked.
>

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