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system of differential couple equations...how?

• To: mathgroup at smc.vnet.net
• Subject: [mg16654] system of differential couple equations...how?
• From: Elio Cecchetto <cecchetto at its.chem.uva.nl>
• Date: Fri, 19 Mar 1999 12:54:04 -0500
• Organization: its
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: system of differential couple equations...how?
    • From: Jurgen Tischer <jtischer@col2.telecom.com.co>