Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?

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- Jan 16th 2011, 11:59 AMNrtNumerical analysis
Hello, i dont know if its possible but can someone simply explain me how to solve a third degree equation with numerical analysis?

- Jan 16th 2011, 12:04 PMpickslides
Are you looking to find the roots of a third degree polynomial with a numerical method?

- Jan 16th 2011, 12:07 PMNrt
Yes.

- Jan 16th 2011, 12:15 PMpickslides
Ok, what methods have you been taught or is this independent learning (happy to suggest some methods), either is fine, do you have a polynomial in particular that needs solving?

- Jan 16th 2011, 02:42 PMNrt
Well, i came across some equations in thermodynamics that was solved with this method it seemed eaiser and faster but i couldnt figure it out on my own. they actually showed us about it in calculus ii last year but i didnt pay much attention since i didnt need it untill now. theres no particular polynominal, feel free to give a simple example.

thanks. - Jan 16th 2011, 03:21 PMpickslides
Well as you studied calculus I would suggest using newton's method. It is an iterative process.

You keep calculating the next value until you see convergence. This value will be the solution.

For the polynomial $\displaystyle \displaystyle f(x)=x^2+2x+7$ choose a starting value in the neighbourhood of the solution, in this case $\displaystyle \displaystyle x_0=-2$ and apply $\displaystyle \displaystyle x_{n+1} =x_n-\frac{f(x_n)}{f'(x_n)}$

First find $\displaystyle \displaystyle x_1$

$\displaystyle \displaystyle x_{1} =x_0-\frac{f(x_0)}{f'(x_0)}= -2-\frac{f(-2)}{f'(-2)}$

What did you get?

__Spoiler__:

Note this value and find $\displaystyle \displaystyle x_2$ repeat - Jan 16th 2011, 03:26 PMNrt
Thank you.