
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

i'm not sure what matlab is, but iterative means you check many values for a variable (your ). it's a guess and check thing. the difficulty is that is not necessarily an integer (Crying).
say you had the equation , and you knew what was. say in this case . a simple iterative method of finding the value of would be to replace with , then , then , and so on, until the value of is greater than ( ). in this case, we would find to be between and .
knowing that is not much of an answer, right? so now is when it gets a little harder. (Headbang)
at this point, you could do a binary search  which means you would guess , because that's right between and . so, , which is less than ( ). now you would guess right between and , so guess . is still less than , so you would guess between and , which is .... you would keep doing this until the error between and was minimal. you get to choose how much error is acceptable.
also, in the case of , you can get an answer algebraically, which is , 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.