*To*: mathgroup@smc.vnet.net*Subject*: [mg11166] Re: [mg11085] Differential Equation evaluation*From*: seanross@worldnet.att.net*Date*: Wed, 25 Feb 1998 03:31:41 -0500*References*: <199802221955.OAA14718@smc.vnet.net.>

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. -- Remove the _nospam_ in the return address to respond.

**References**:**Differential Equation evaluation***From:*Spooky <SLKBC@cc.usu.edu>