(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I have attached the actual problem as a picture (hope that is ok).

X_{n+1}= 12/(1+X_{n}), r=3

For each of the following iteration schemes the sequence x_{n}will converge to the given value of r provided the

initial value x_{0}is sufficiently close to r. In each case determine the order of convergence.

2. Relevant equations

I have the equation:

|e_{n+1}/e_{n}^{α}| ≈ C

e_{n}= r - x_{n}

e_{n+1}= r - x_{n+1}

3. The attempt at a solution

I have attempted to substitute x_{n+1}into the last equation and then divided terms, but I end up with a final result of 3/(1+x_{n}). I cannot understand how to find the order of convergence from this. Any hints would be appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Order of Convergence: Iteration Scheme

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**