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MathGroup Archive 1998

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Re: Differential Equation evaluation



Spooky wrote:
> 
>         Hi, I am new to Mathematica and just bought verison 3.0, I am trying to
> solve a differential equation of the form:
> 
> F''' + F*F' + 1 - (F')^2 == 0
> 
> with boundry conditions for F, F', F'' at 0 and F' at infinity, is there
> a way to handle this?  When I try this, if I include that boundry
> condition at infinity  with the others, Mathematica tells me I have to
> many constraints, if I leave it off I can solve it, if I leave off the
> condition for F' at 0, it tells  me it can't find the value of variable
> at the variable at 0.  So, my question, is how do I handle this in
> Mathematica.
> 

	Due to the F*F' and (F')^2 term, this equation is a nonlinear
differential equation.  They are very difficult, in general, and DSolve
only can handle a few of them.  With a boundary condition at infinity,
you effectively rule out a numerical solution.  Someone at Wolfram
could probably clarify this, but I am guessing that DSolve does not
cover your particular Nonlinear DE and you are getting error messages
from whatever subroutine gives up on it first.
	It sounds like you may have to cheat to solve this one.  If you could
give us a little more information about your problem like, what is the
boundary condition at infinity etc, perhaps we could think of a way to
skip around all the difficulties.  Be aware, though, that the vast
majority of algebraic expressions can't be solved by algebra, the vast
majority of integrals can't be solved in closed form and the vast
majority of differential equations can't be solved in closed form
either.  Numerical solutions often involve some programming on your own
since it is very difficult to write a routine general enough that it
can figure out what to do on its own.


> I have another general question about the system.  I am using version
> 3.0 for Win95.  Often, if I make a syntax error, Mathematica will print
> me an error message but then I can't be certain that any subsequent
> error messages are valid.  The reason I say this is that I  will find
> my error, correct it and then I will get another error message upon
> evaluation.  After struggling with it for  a while, I will close it and
> re-enter and what gave me errors prior to re-entering, evaluate fine.
> Is there some way to be sure that  the errors are valid?
> 

I have been dissappointed with mathematicas error messages and find that
unless there is only one or two that none of them are very helpful. 
Mathematica can rarely tell the difference between a missing quote and
a missing bracket etc.  I always test my code one line at a time before
executing it all.  I have inadvertently created infinte loops of error
messages by small syntax errors when I forgot to test.


-- 
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