It looks simple but

  • Thread starter kaniello
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  • #1
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Hallo,
I ended up with this PDE:

du/dt + A*u² =C

A and C are constants and U is only function of time.
It looks simple but...
Can someone help me?
Thanks a lot in advance
 

Answers and Replies

  • #2
CompuChip
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It is a Riccati equation, and indeed it is slightly more tricky than you may initially think.
 
  • #3
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Thank you so much!! That was a quick answer!
 
  • #5
@dextercioby. That would work to solve for a function of u (e.g. f(u) = ...) , but kaniello here is solving for the function u(t) that satisfies the ODE... a much tricker problem that satisfies the riccati equation.
 
  • #6
dextercioby
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Hmmm

[tex] \frac{du}{dt} = C-Au^2 \Rightarrow \int dt = \int\frac{du}{C-Au^2} \Rightarrow...[/tex]

??
 
  • #7
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..which would be
tanh⁻1([itex]\sqrt{a/c}[/itex] / (a/c).
I am currently studying the article from CompuChip and reference given there. Probably this is the solution that comes out from the Riccati equation setting q1=0, q0 and q2= const.
 
  • #8
AlephZero
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@dextercioby. That would work to solve for a function of u (e.g. f(u) = ...) , but kaniello here is solving for the function u(t) that satisfies the ODE... a much tricker problem that satisfies the riccati equation.
It is a Riccati equation, and indeed it is slightly more tricky than you may initially think.
The Riccati equation is only "tricky" in the general case - for example when C in the OP's equation is replaced by something like [itex]Ct^n[/itex]

As dextercioby said, this special case is straighforward to integrate.
 

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