Real Work Application of "Newthon-Raphson" method.

arianabedi

1. The problem statement, all variables and given/known data
Hi, an undergrad engineering (presentation) question:

As a presentation, I am (plus a group mate) tasked to present a real world application of the Newthon-Raphson method (of finding a root). Now I know that we can also find minima/maxima of a graph with it by modifying the equation (which i would like to avoid since we actually haven't covered that, its from my own research). However I can't think of any real world application where Newton-Raphson is the best way to find the root of a graph.

Can anyone give me some ideas on where this method could be used in say the "real world"?

I guess that main thing I would like to know is where do we actually use a root of a number in engineering? Since all I've done is principles with no practical use.

2. Relevant equations

Newthon-Raphson iteration formula:
[tex] x_{n-1}=x_{n}-\frac{f(x_{n})}{f'(x_{n})} [/tex]
...phew that took a while to write :D

3. The attempt at a solution

I tried several simple graphs (speed/time , acceleration/time and some other high school physics stuff but in all cases they didn't seem like a real world application since there was always another way of finding say the "x" axis's intercept.

*NOTE:
By the time I reached here in the tread, I thought of maybe relating it to say some growth of bacteria which multiplies by it self (haven't done any maths on it yet) but that thats all Biology. Or maybe the inverse square rule for gravitational pull; but then again I'm not sure where we use it (NASA?) i'll have to do more research.

arianabedi

Well not really engineering related but i found this question from [HERE] but sadly its not engineering related, seems more like finance/accounting to me:

"It costs a firm C(q) dollars to produce q grams per day of a certain chemical, where
C(q) = 1000 + 2q + 3q2/3
The firm can sell any amount of the chemical at $4 a gram. Find the break-even point of the firm, that is, how much it should produce per day in order to have neither a profit nor a loss. Use the Newton Method and give the answer to the nearest gram."

TIME TO SOLVE!

hunt_mat

I used Newtons method to compute shock polars for materials, does that help?

jimbobian

It says in my textbook that it was originally developed by Newton to solve Kepler's Equation about the orbit of a body which, ignoring the real world meaning of the variables, is

[itex]x-ksinx=nt[/itex]

Surely this would be classified as a "real world use", even if I can't find proof of the history of its conception anywhere other than this book!

arianabedi

Well this seems like a "real world use" and i'll have to solve it first. unfortunately this presentation of mine is being a pain in the neck!

*EDIT* forgot to mention, could you please give me an example of using this? i'm currently googling it but just in case i don't find anything useful.

thanks for the help thou.

arianabedi

Hey very sorry for the late reply, this tread just slipped my mind. Well it seems like a perfect real world engineering example but it would be fantastic if you could provide me with a simple example of doing that. Right now I'm reading on shock polars since i'll have to explain what they are (i have no idea what they are myself).