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Homework Help: Implicit numerical differentiation

  1. May 26, 2010 #1
    1. The problem statement, all variables and given/known data

    I am using Crank–Nicolson to solve a logistic function, modeling population growth.
    To get the next time step, I have to solve a quadratic equation.
    The problem is that i get two solutions for y(i+1). Does it mean that I am doing it wrong?
    If not, can I just pick the solution that is closest to y(i)?
     
  2. jcsd
  3. May 27, 2010 #2
    Example:
    Logistic growth, implicit scheme, not Crank-Nicolson.

    [tex]\frac{u_{n+1}-u_n}{\Delta t} = n_{n+1}(1 - \frac{u_{n+1}}{R})[/tex]

    R is the carrying capacity

    Here I have to solve a quadratic equation to find [tex] u_{n+1}[/tex]
     
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