0
$\begingroup$

I am struggling making a cobweb diagram for the function $$x_{t+1}=8x_t/{1+2x_t}$$

So I understand when making the cobweb diagram, that I have to draw the line $y=x$

But where I have trouble understanding is how to draw the function in the graph. I am given the point $x_0 =0.5$ So I plug this into the function and get $2 = x_1$ and then I keep plugging in points. Do I graph points like $.5,2$ or $0,.5$?

$\endgroup$
  • $\begingroup$ I hope this doesn't come across as advertising. In the UK a lot of schools use a piece of software called Autograph. It draws cobweb diagrams for you... and shows Newton-Raphson working, too. $\endgroup$ – tomi Mar 13 '15 at 9:24
2
$\begingroup$

Let the expression on the right be $g(x)$. The method converges (sometimes) to the solution of the equation $x=g(x)$.

The cobweb diagram illustrates the movement from first guess $x_0$ to second guess $x_1$ etc.

Draw a line from $(x_0,0)$ up to $(x_0,x1)$.

Then across to $(x_1,x_1)$.

Then up or down to $(x_1,x_2)$.

Then across to $(x_2,x_2)$.

Etc

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.