System of second-order nonlinear ordinary differential equations

*To*: mathgroup at smc.vnet.net*Subject*: [mg128657] System of second-order nonlinear ordinary differential equations*From*: killer_katschinski <jan.hildenbeutel at gmail.com>*Date*: Wed, 14 Nov 2012 01:29:46 -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

Hello, I'm new to this forum and also to Mathematica, so please treat me gentle :) I would solve numerically the velocity profiles of a rotating disk. Thefore following system must be solved for the 3 (nondimensional) unknown velocity-functions F(eta), G(eta) and H(eta), with eta=nondimensional wall distance (see "Boundary Layer Theory" by H. Schlichting): 2F+H'=0 F^2+F'*H-G^2-F''=0 2F*G+H*G'-G''=0 with the follwing boundary conditions: F(x=0)=0 G(x=0)=1 H(x=0)=0 F(x->\inf)=0 G(x->\inf)=0 I tried to implement the problem into Mathematica with the numerical solver : NDsolve[{2*F[eta] + H'[eta] == 0, (F[eta])^2 + F'[eta]*H[eta] - (G[eta]^2 - F''[eta] == 0, 2*F[eta]*G[eta] + H[eta]*G'[eta] - G''[eta] == 0}, {F[0] == 0, G[0] == 1, H[0] == 0, F[1000000] == 0, G[1000000] == 0}, {eta, 1000000}] Plot[Evaluate[{F[eta], G[eta], H[eta]} /. s], {eta, 0, 5}, PlotStyle -> Automatic] I did not arrive to any solution but to many many errors. If you could give me any hint I would be really thankful! Best regards killer_katschinski

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