Re: Non linear diff eq
- To: mathgroup at smc.vnet.net
- Subject: [mg15569] Re: Non linear diff eq
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Tue, 26 Jan 1999 13:44:47 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <78077s$ag7$3@dragonfly.wolfram.com>
- Sender: owner-wri-mathgroup at wolfram.com
Hi Fancisco,
you will not find a closed. You can't solve the equation numerical
because the numerical solvers require that the right hand side has
smooth derivatives. But You can come closer to the solution with
deqn=x''[t]+Abs[x[t]]==0;
deqn1= (Expand[x'[t]*#] & /@ deqn) /. a_+b_==0 :> a==-b;
deqn2=Integrate[Expand[#],{t,0,tau}] & /@
deqn1 /.HoldPattern[Integrate[Abs[x_[t_]]*x_'[t_],{t_,a_,b_}]] :>
Dot[{1,-1},(x[t]^2*Sign[x[t]] /. {{t->b},{t->a}}) ]
deqn3=Solve[deqn2 /. tau->t /. x[0]->0,x'[t]]/. Rule -> Equal//Flatten
Now it is up to you (because only you know if a> 0 or a<0) to solve the
two equations.
Hope that helps
Jens
Fancisco Gutierrez wrote:
>
> Hi! I have the following nonlinear diff. eq.: x'' + Abs[x]=0, t element
> of [0,1], with these boundary conditions: x[0]==0, x[1]==a.
>
> How can I work it out with Mathematica?
>
> thanks!
>
> Francisco Gutierrez