Help, How do I stop my iteration from going when it gets the answer?

Hello good day, below is my code and I am using Netwons method of iteration.

I have the code typed out, but I dont know how to stop the code when it gets its answer...it keeps running with the answer 25.1327 over and over.

Thank you

function c = newton(f,fd,x0,tol)

%Given information 
g = 9.81; % Gravity
h = 1; % Water depth in meters
H = .2; % Wave height in meters
T = 2; % Wave period in seconds 

f = @(L) ((L-(g/(2*pi)))*(T^2)*(tanh((2*pi*h)/L))); % Linear dispersion 
fd = @(L) 1+(((g*h*T^2)/(L^2))*sech((2*pi*h)/(L).^2)); % First derivative of Linear dispersion
tol = 0.0001 % how much tollarance 
x0 = 0.001 % inital guess 

L =x0;
y = f(L);

while abs (y) > tol % While loop to do the iterative method
    L =L - y/fd(L); % Newtons iterative method. 
    y = f(L)% function of Linear dispersion 
             
       end
end

[Mario Malic]

while abs (y) > tol % While loop to do the iterative method
    L =L - y/fd(L); % Newtons iterative method. 
    y = f(L)% function of Linear dispersion 
end

Loop does what you tell it to do. Is abs(y) bigger than tol? According to your result, 25.1327 is much higher than tol obviously. Something's missing in your code/implementation of iterative method, and maybe it's L that does not get updated.

Answer 1

[Star Strider]

Put in a condition that compares subsequent results with ‘tol’. Change the loop to something like this:

yprev = Inf;
yd = Inf;
while abs (yd) > tol % While loop to do the iterative method
    L =L - y/fd(L); % Newtons iterative method.
    y = f(L)% function of Linear dispersion
    yd = y-yprev;
    yprev = y;
end

so the full code is then:

%Given information
g = 9.81; % Gravity
h = 1; % Water depth in meters
H = .2; % Wave height in meters
T = 2; % Wave period in seconds
f = @(L) ((L-(g/(2*pi)))*(T^2)*(tanh((2*pi*h)/L))); % Linear dispersion
fd = @(L) 1+(((g*h*T^2)/(L^2))*sech((2*pi*h)/(L).^2)); % First derivative of Linear dispersion
tol = 0.0001 % how much tollarance
x0 = 0.001 % inital guess
L =x0;
y = f(L);
yprev = Inf;
yd = Inf;
while abs (yd) > tol % While loop to do the iterative method
    L =L - y/fd(L); % Newtons iterative method.
    y = f(L)% function of Linear dispersion
    yd = y-yprev;
    yprev = y;
end

This worked when I ran it. Check to be certain it gives the correct result.

Note that ‘c’ is never calculated. It would likely be best for your function to return the actual result you want.

[Nicholas Deosaran]

Thank you, that was able to stop the code.

[Nicholas Deosaran]

But is there a way to just get one answer ?

[Star Strider]

My pleasure!

I am not certain what you are asking. The result is returned in ‘y’, so the output of your function must be ‘y’, not ‘c’ (that is never calculated).

[Nicholas Deosaran]

In my while-loop, I want to compare the difference of the wavelength (L) between two iterations.

How would I do that?

Thank you.

[Nicholas Deosaran]

At the end L is to equall or be 5.2154

[Star Strider]

Nothing with respect to ‘L’ was ever stated.

I have absolutely no idea what you are doing.

I would change the loop to something like this, storing the value of ‘L’ in each iteration:

yprev = Inf;
yd = Inf;
k = 1;
while abs (yd) > tol % While loop to do the iterative method
    L = L - y/fd(L); % Newtons iterative method.
    y = f(L); % function of Linear dispersion
    yd = y-yprev;
    yprev = y;
    Lv(k) = L;
    k = k + 1;
end
Lv

Note that ‘L’ quickly becomes negative. I leave the rest to you, since this appears to be homework.

Answer 2

[David Hill]

If you graph the function you will see the problem at L=0

g = 9.81;
h = 1;
T = 2;
f=@(L) L-g/(2*pi)*T^2*tanh(2*pi*h./L);
L=-.0001:.000000001:.0001;
plot(L,f(L));