# Thread: Iterative methods

1. ## Iterative methods

Hello,

I am not a math major but an ocean scientist. I am trying to solve an equation for wave motion under water and I need help.

I would like to use Matlab to solve for a variable using an iterative approach but I have to understand what that really means before I do that. The equation is:

Where z, v, and U are known integers, * = multiply, / = divide

I would like to find u_star,

U = (5.5/u_star) + (2.5*(ln((u_star*z)/v)))/u_star

Do you have any suggestions about which iterative method would work best?
Do you have any suggestions about where to go to find a SIMPLE explanation about the application of an iterative method online?
Should I not do this because it is really complicated?

Thank you for reading my post and thank you for any help/suggestions you have to offer, they are greatly appreciated.

Sophie

2. i'm not sure what matlab is, but iterative means you check many values for a variable (your $\displaystyle u\_star$). it's a guess and check thing. the difficulty is that $\displaystyle u\_star$ is not necessarily an integer .

say you had the equation $\displaystyle 2^y = 3^x$, and you knew what $\displaystyle x$ was. say in this case $\displaystyle x = 5$. a simple iterative method of finding the value of $\displaystyle y$ would be to replace $\displaystyle y$ with $\displaystyle 0$, then $\displaystyle 1$, then $\displaystyle 2$, and so on, until the value of $\displaystyle 2^y$ is greater than $\displaystyle 3^5$ ($\displaystyle 243$). in this case, we would find $\displaystyle y$ to be between $\displaystyle 7$ and $\displaystyle 8$.

knowing that $\displaystyle 7 < y < 8$ is not much of an answer, right? so now is when it gets a little harder.

at this point, you could do a binary search - which means you would guess $\displaystyle 7.5$, because that's right between $\displaystyle 7$ and $\displaystyle 8$. so, $\displaystyle 2^{7.5} = 181.blahblah$, which is less than $\displaystyle 3^5$ ($\displaystyle 243$). now you would guess $\displaystyle y$ right between $\displaystyle 7.5$ and $\displaystyle 8$, so guess $\displaystyle y = 7.75$. $\displaystyle 2^{7.75}$ is still less than $\displaystyle 243$, so you would guess between $\displaystyle 7.75$ and $\displaystyle 8$, which is $\displaystyle 7.875$.... you would keep doing this until the error between $\displaystyle 2^y$ and $\displaystyle 3^5$ was minimal. you get to choose how much error is acceptable.

also, in the case of $\displaystyle 2^y = 3^5$, you can get an answer algebraically, which is $\displaystyle y=\frac{ln(3^5)}{ln(2)}$, however, in the case of your equation, i don't see an immediate algebraic solution. if you do find one, i would love to see it.

if this is confusing or if you would like more explanation about a binary search feel free to ask questions. a binary search is just one iterative method you might use, i'm sure you could find a better (faster) way.