Dealing with nonlinear ODE with contraint equations

enoch · August 24, 2010, 14:52

I'd like to solve the below highly nonlinear ODEs with constraint equations. Eq 1 is a 2nd order ODE, so I need two BCs where only one BC is specified and the other should be determined by Eq2. I have no clue on how to approach this kind of problem and don't know how to use Eq 2. I really appreciate that if you could give me some helps to resolve those constraints in terms of numerics. Thanks.

Governing Equations
--------------------
nu: 2*(1+nu+nu^2)*nu'*nu'' + (2*nu+1)*(nu')^3 = 0, (Eq 1)

Boundary Conditions
-------------------
nu(-1) = 0.2, nu(1) = alpha (determined by Eq2)

Constraints
-------------
N=integral( nu*dY ) dY from Y=-1 to Y=1, (Eq 2)
Eq 4 should be used to determine alpha

otd · August 25, 2010, 09:25

N and U appear in the equations but are not mentioned in your description. U' also appears. Something must be missing.

You might try again to specify your problem.

August 24, 2010, 14:52	Dealing with nonlinear ODE with contraint equations	#1
enoch Member Jeong Kim Join Date: Feb 2010 Posts: 42 Rep Power: 16	I'd like to solve the below highly nonlinear ODEs with constraint equations. Eq 1 is a 2nd order ODE, so I need two BCs where only one BC is specified and the other should be determined by Eq2. I have no clue on how to approach this kind of problem and don't know how to use Eq 2. I really appreciate that if you could give me some helps to resolve those constraints in terms of numerics. Thanks. Governing Equations -------------------- nu: 2(1+nu+nu^2)nu'nu'' + (2nu+1)(nu')^3 = 0, (Eq 1) Boundary Conditions ------------------- nu(-1) = 0.2, nu(1) = alpha (determined by Eq2) Constraints ------------- N=integral( nudY ) dY from Y=-1 to Y=1, (Eq 2) Eq 4 should be used to determine alpha Last edited by enoch; August 25, 2010 at 09:51.

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August 25, 2010, 09:25		#2
otd Member private Join Date: Mar 2009 Posts: 74 Rep Power: 17	N and U appear in the equations but are not mentioned in your description. U' also appears. Something must be missing. You might try again to specify your problem.