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