MathGroup Archive 2013

[Date Index] [Thread Index] [Author Index]

Search the Archive

meaningful solution to the differential eqn

  • To: mathgroup at smc.vnet.net
  • Subject: [mg120044] meaningful solution to the differential eqn
  • From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
  • Date: Wed, 6 Mar 2013 05:56:12 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com
  • Delivered-to: l-mathgroup@wolfram.com
  • Delivered-to: mathgroup-newout@smc.vnet.net
  • Delivered-to: mathgroup-newsend@smc.vnet.net

I have been trying to get a meaningful solution to the differential eqn. for the voltage and current in an inductor:
V[t] == -L i'[t].  For smooth voltage waveforms, the current function is well-behaved and a reasonable solution.  But when V[t] is a piecewise function, either my own, or one of the built-in ones, such as SquareWave, the solutions obtained are unreasonable.  They may satisfy the differential equation, but they increase in magnitude without limit.  I tried integrating the SquareWave[t] Mathematica function, and I could see why DSolve was probably having a problem.  The square wave has values +1 or -1 on each half-cycle.  Integrate[] sees these constants in the Piecewise statement and simple-mindedly replaces them with +t and -t.  So as t gets larger or smaller, the integral(s) yield ramp functions that alternate in sign during every half-cycle of the square wave.  What Integrate should yield is a positive-going ramp on the + half-cycle, and a decreasing positive-valued ramp on the - half-cycle of the square wave.  The correct function should be the sum of SquareWave[t]*dt over
  t.  The
  integrals created over each (continuous, differentiable) half-cycle should then be added to create a new function.  I can't figure out how to implement Integrate on piecewise functions like this.  Does anyone know how?

P.S.  I couldn't find a way to search MathGroup postings from the group's pages, so I may be posting an already solved problem.  If so, please let me know how I can use the group more efficiently.


Yes somebody knows. This:

Plot[SquareWave[x], {x, 0, 5}]

is the plot of a SquareWave. Evaluate it. And this:

f[z_] := Integrate[SquareWave[x], {x, 0, z}];

is a definition of the integral of the square wave. One may now plot it. Evaluate this:

Plot[f[z], {z, 0, 5}]

It behaves exactly as you described it should.




Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG

Office phone :  +352-2454-2566
Office fax:       +352-2454-3566
mobile phone:  +49 151 52 40 66 44

e-mail: alexei.boulbitch at iee.lu






  • Prev by Date: Re: Problem in solving Differential Equation
  • Next by Date: Re: Why mathematica can't solve this non linear equation
  • Previous by thread: NSum[(-1)^n*(n^(1/n)-a),{n,Infinity}] and the like
  • Next by thread: Re: Power Law with singularity' regression - error