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Re: Solving nonlinear coupled differential equations in Mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95332] Re: Solving nonlinear coupled differential equations in Mathematica
  • From: Torsten Hennig <Torsten.Hennig at umsicht.fhg.de>
  • Date: Thu, 15 Jan 2009 06:14:44 -0500 (EST)

> Here is a set of equations I would like to solve
> 
> y''[x]==y+z'[x]
> z[x]^3=y'[x]+3
> 
> With boundary conditions of y[1]==2 and y[0]==3
> 
> Using NDSolve on these equations, Mathematica says
> the order of the
> equations is 3 and it has only 2 initial conditions.
> But the order of
> this system of equations is 2 as far as I see (since
> order is defined
> as the highest derivative)
> 
> When I do try to put another boundary condition in
> like z[0]==0
> Mathematica spits out that it cant solve for the
> derivatives and is
> using a mass matrix method (error:ntdvmm) and then it
> says that it has
> significant errors (error:berr) and will return the
> best solution
> found.
> 
> Any help on this matter will be greatly appreciated.
> Thanks
> 

z^3 = y' + 3  ->  3*z^2*z' = y''
Inserting in the first equation gives
3*z^2*z' = y + z'
or
z'=y/(3*z^2-1)

So you should solve the following two equations

(I)  z'=y/(3*z^2-1)
(II) y'=z^3-3

with appropriate boundary conditions.

Best wishes
Torsten.


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