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Re: Differential Eq.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106518] Re: [mg106478] Differential Eq.
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Fri, 15 Jan 2010 03:18:42 -0500 (EST)
  • References: <201001141047.FAA19753@smc.vnet.net>

Jamil Ariai wrote:
> Hi All,
> 
> Can anybody kindly tell me how I can solve the following differential equation, with (x[0], x'[0]) = (0, 0):
> 
> x''[t] -x[t] + g[t] = 0,
>  
> where
> 
> g[t] = b*v, for x'[t] > v,
> g[t] = b*(x'[t]-u), for Abs[x'[t]-u] < v, and
> g[t] = -b*v.
> 
> Take b = 5, v = 0.2, and u = 0.1. Draw x[t] vs t, and x'[t] vs x[t].
> 
> Thanks.
> 
> J. Ariai 		 	   		 

Could set it up as below.

soln = First[
   With[{b = 5, v = 0.2, u = 0.1},
    With[{gt =
       Piecewise[{{b*v, x'[t] > v}, {b*(x'[t] - u),
          Abs[x'[t] - u] < v}}, -b*v]},
     NDSolve[{x''[t] - x[t] + gt == 0, x[0] == 0, x'[0] == 1.15},
      x[t], {t, 0, 3}]]]]

If your initial derivative is one or less, the default handling seems to 
run into trouble at one of the switches. I do not know why. Possibly 
some Method or other settings can improve on that.

Daniel Lichtblau
Wolfram Research


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