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MathGroup Archive 2004

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Re: Re: Re: newbie question DSolve (revisited)

  • To: mathgroup at smc.vnet.net
  • Subject: [mg52147] Re: [mg52118] Re: [mg52090] Re: newbie question DSolve (revisited)
  • From: yehuda ben-shimol <benshimo at bgu.ac.il>
  • Date: Fri, 12 Nov 2004 02:14:03 -0500 (EST)
  • References: <cmppui$mll$1@smc.vnet.net> <200411100945.EAA11259@smc.vnet.net> <200411110952.EAA28827@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I tried to use LaplaceTransform for your problem and the result agree 
with the message given by DSolve. 
Using LaplaceTransform you you finally get a result that y'[0] depends 
on y[d] (or the opposite), so you really need another external 
constraint for that matter (the DiracDelta function "samples" y at its 
singular point).
do you have any such information ?
yehuda

Pratik Desai wrote:

>Thank you Dr. Hintze for your response,
>
>I tried your suggestion unfortunately, Mathematica gives me another error it 
>is as follows
>
>In[10]:=
>DSolve[{y''[x] - lamda^2*y[x] == DiracDelta[x - d]*y[d], y[0] == 0,
>y[l] == 0}, y[x], x]
>
>  (DSolve::"litarg"),  "To avoid possible
>    ambiguity, the arguments of the    dependent variable in (the equation) 
>should literally match the independent variables".
>
>
>Thanks again for your reply again Dr Hintze,
>
>
>
>Pratik Desai
>
>
>
>----- Original Message ----- 
>
>From: "Dr. Wolfgang Hintze" <weh at snafu.de>
To: mathgroup at smc.vnet.net
>To: mathgroup at smc.vnet.net
>Subject: [mg52147] [mg52118] [mg52090] Re: newbie question DSolve
>
>
>  
>
>>If you replace DiracDelta[d - x]*y[x] by the equivalent DiracDelta[d -
>>x]*y[d] then your equation can be solved as follows (with just one minor
>>error message appearing twice, which can be ignored)
>>
>>In[1]:=
>>s = DSolve[{-y[x] + Derivative[2][y][x] == DiracDelta[d - x]*y[d], y[0]
>>== 0, y[L] == 0}, y[x], x]
>>
>>From In[1]:=
>>DSolve::"nvld" : "The description of the equations appears to be
>>ambiguous or \
>>invalid."
>>
>>Out[1]=
>>{{y[x] -> 1/2*E^(-d - x)*(-((E^(2*x)*((-1 + E^(2*d))*UnitStep[-d] -
>>(E^(2*d) - E^(2*L))*UnitStep[-d + L])*y[d])/
>>        (-1 + E^(2*L))) + ((E^(2*L)*(-1 + E^(2*d))*UnitStep[-d] -
>>(E^(2*d) - E^(2*L))*UnitStep[-d + L])*y[d])/
>>       (-1 + E^(2*L)) - E^(2*d)*UnitStep[-d + x]*y[d] +
>>E^(2*x)*UnitStep[-d + x]*y[d])}}
>>
>>From In[2]:=
>>DSolve::"nvld" : "The description of the equations appears to be
>>ambiguous or \
>>invalid."
>>
>>Extracting the solution to u[x]
>>
>>In[4]:=
>>u[x_] = y[x] /. s[[1]]
>>
>>you can Plot it, after assigning numeric values to all relevant 
>>quantities:
>>
>>In[6]:=
>>L = 1; d = 0.5; y[d] = 1;
>>Plot[u[x], {x, -1, 4}, PlotRange -> {{-1, 5}, {-2, 1}}];
>>
>>Hope this hepls
>>Wolfgang
>>
>>
>>Pratik Desai wrote:
>>
>>    
>>
>>>Hello all
>>>
>>>I am trying to use DSolve to solve a ode with discontinuity in it (wave
>>>equation with a viscous damper injected at a location d)
>>>
>>>This is what i am using
>>>
>>>DSolve[{y''[x]-lamda^2*y[x]==DiracDelta[x-d]*y[x],y[0]==0,y[L]==
>>>=0},y[x],x]
>>>
>>>the problem I am facing is that
>>>
>>>y[x] on the right hand side (next the delta function) varies w.r.t to
>>>the location
>>>
>>>y[x]==y[x]&& 0<=x<=d
>>>y[x]==y[L-x]&&d<=x<=L
>>>
>>>I can solve the above equation without the y[x] coupled to the delta
>>>function
>>>
>>>Please advise and thanks in advance,
>>>
>>>
>>>Pratik Desai
>>>
>>>
>>>ps: This is my third attempt at posting my query, I hope this time it
>>>makes it to the list :)
>>>
>>>
>>>


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