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MathGroup Archive 2002

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RE: how to solve for periodic solution?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg35736] RE: [mg35716] how to solve for periodic solution?
  • From: "DrBob" <majort at cox-internet.com>
  • Date: Sun, 28 Jul 2002 03:32:10 -0400 (EDT)
  • Reply-to: <drbob at bigfoot.com>
  • Sender: owner-wri-mathgroup at wolfram.com

Try algebra:

Solve[A[t] == S[t + P] - Log[2]/halflife*A[t], A[t]]

{{A[t] -> S[P + t]/ (1 + Log[2]/halflife)}}

That works no matter what values S takes on, so your one equation won't
let you solve for S between t1 and t2.

If A is known and you're solving for S, it's still algebra, but A would
have to satisfy the boundary conditions.

Bobby Treat

-----Original Message-----
From: tom [mailto:theiman at comcast.net] 
To: mathgroup at smc.vnet.net
Subject: [mg35736] [mg35716] how to solve for periodic solution?

Hi,

I have no clue as to how to proceed to solve the equation below.
Any ideas on how to solve for the periodic solution of this equation
would be most appreciated!! Thankyou!!

A(t)=S(t+P)-(ln(2)/halflife)*A(t)

S(t+P) = S(t)  if t1<t<t2
S(t+P) = 0 otherwise

where P is the period of the system
t is the time at which a sample is taken
t1 is the beginning of a discontinuity
t2 is the end of a discontinuity
A(t) is the abundance at time t

I want to fit data to the resulting equation and find t1 and t2

Sincerely,

Tom





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