[Date Index]
[Thread Index]
[Author Index]
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**
| |