# Homework Help: Implicit numerical differentiation

1. May 26, 2010

### MaxManus

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. May 27, 2010

### MaxManus

Example:
Logistic growth, implicit scheme, not Crank-Nicolson.

$$\frac{u_{n+1}-u_n}{\Delta t} = n_{n+1}(1 - \frac{u_{n+1}}{R})$$

R is the carrying capacity

Here I have to solve a quadratic equation to find $$u_{n+1}$$