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Re: system of differential couple equations...how?

• To: mathgroup at smc.vnet.net
• Subject: [mg16814] Re: [mg16654] system of differential couple equations...how?
• From: Jurgen Tischer <jtischer at col2.telecom.com.co>
• Date: Tue, 30 Mar 1999 02:35:16 -0500
• Organization: Universidad del Valle
• References: <199903191754.MAA09820@smc.vnet.net.>
• Sender: owner-wri-mathgroup at wolfram.com

Elio,
if I don't like to forget about the conditions in 2L, I still have to,
as far as I see. There is an error(?) in your NDSolve (besides the
missing comma), it reads [Pi] in the first equation. I corrected it (?)
to Pi and had no problem with the standard shooting to get a solution.
But: If you replace th by 0& your system reduces to phi''[z] == 0 which
is a lot easier to solve. So you have the solution th=0& y phi=Pi/(4L)&,
which by the way solves your conditions in 2L as well.

Jurgen

Elio Cecchetto wrote:
> 
> Does anyone has any idea how I can solve the following system of two non
> linear equation ith the functions: th[z] and phi[z]?
> I would like to skip the trivial solution th[z]=0
> 
> I tried also with a shooting technique but is hopeless
> 
> L=N[4 10^-6];Ea=(5.38-4.95);V=4.2
> k1=N[6.4 10^-12];k2=N[3.8 10^-12];k3=N[8.11 10^-12]
> 
> solution=NDSolve[{-1/(4 Pi)(Ea V^2 Cos[th[z]] Sin[th[z]])+ 2 Pi(k2+(k2 -
> k3) Cos[2th[z]])
>                   Sin[2th[z]] phi'[z]^2 - 2(k1 - k3) Pi Sin[2 th[z]]
> th'[z]^2 + 4 k1 Pi Cos[th[z]]^2
>                    th''[z] + 4 k3 [Pi] Sin[th[z]]^2 th''[z] == 0
> 
>   -Cos[th[z]] (-2(k2 + (k2 - k3) Cos[2 th[z]]) Sin[th[z]] phi'[z] th'[z]
> +
>      Cos[th[z]] (k2 Cos[th[z]]^2 + k3 Sin[th[z]]^2) phi''[z]) == 0,
>   th[0] == 0,
> th'[L] == 0,
> phi[0] == 0,
> phi[L] == Pi/4,
> th[2L] == 0,
> phi[2L] == Pi/2},
>                  {th, phi} {z, 0, 2L}];
> 
> Plot[{th[z]*90/1.5 /. solution, phi[z]*90/1.5 /. solution}, {z, 0, 2L},
> PlotRange -> All,
>         PlotStyle -> {RGBColor[1, 0, 0], RGBColor[0, 0, 1]}];
> 
> If you like you can forget the conditionsin 2L : th[2L] == 0, phi[2L] ==
> Pi/2
> 
> thanks to anyone who can help
> 
> Elio Cecchetto

• References:
  • system of differential couple equations...how?
    • From: Elio Cecchetto <cecchetto@its.chem.uva.nl>