How to plot graphic with 2 variables function

I use these codes:

clear
clc

H=2.5 
h=11 
T=9 
w=2*pi/T
k1=1 
g=9.81

%This is Newton's Rhapson Method
x1=k1*h;
TOL=1.0e-5;
f=@(x) x*tanh(x)-w^2*h/g;
df=@(x) tanh(x)+(x/(cosh(x))^2);
fprintf ('Iteration root f(root) \n')
if df(x1) ~= 0
    for i=1:1000
        x2=x1-(f(x1)/df(x1));
        fprintf ('ke-%d %.5f %.5f\n', [i,x1,f(x1)]')    
        if abs (f(x2)) < TOL
            break
        end
        x1=x2;
    end
end
fprintf ('root: %f\n',x1')
fprintf ('Number of iteration: %f\n', i')
L=2*pi()*h/x1 
% PLOT
kgel=x1/h 
xi=-L/4 
xf=5*L/4 
t=0 
fplot(@(x) H/2 * cos(kgel.*x - w*t),[xi xf],'Color','c','LineWidth',1.5)
title('u and w in t=0')
xlabel('x axis')
ylabel('z axis')
grid
nx1=L/4
nx2=3*L/4
nx3=L/2
nx4=L
hold on
fplot(@(z) (H*w/2)*(cosh(kgel*(h+z))/sinh(kgel*h))*cos(kgel*nx1-w*t),[-h H])
fplot(@(z) (H*w/2)*(sinh(kgel*(h+z))/sinh(kgel*h))*sin(kgel*nx1-w*t),[-h H])
hold off

What should i do?

went wrong like this:

[Dyuman Joshi]

There are undefined variables in your code, thus we can not run it to check the results.

Please update the code.

[Bagus]

Sorry. I already updated the code. thank you

[Dyuman Joshi]

Okay, so you have to plot u (x-velocity) and v (z-velocity) vs x,z, and t? If so, how is that a 2D plot?

If not, please explain further.

[Bagus]

Thanks for your response. I don't know what I have to do. I thought I can use the implicit function.

x and t input on those equations are not variables, there are constants. so I just have to make the velocity equation (u and w equations) to be just a function of z.

[Bagus]

Sorry. I want to make the equation just a function of z, by that so I put the values of x and t and it is just a constant number, it is not changing. the only value that variate is z. so the functions are just a function of z.

[Bagus]

And z is in the y-axis according to the equation and my calculation. So how can I plot a function that has input on a variable in the y-axis? or there is another way to do that?

[Dyuman Joshi]

How did you come to the conclusion that u and v at t=0 are given by

H/2 * cos(kgel.*x - w*t)

The magnitude of u (~10^-16) is quite small compared to v (~1), see the plots at the end. Are the numerical values all correct? I suggest you to cross-check.

H=2.5;
h=11;
T=9;
w=2*pi/T;
k1=1;
g=9.81;

%This is Newton's Rhapson Method
x1=k1*h;
TOL=1.0e-5;
f=@(x) x*tanh(x)-w^2*h/g;
df=@(x) tanh(x)+(x/(cosh(x))^2);

Also, it's not clear what you want to do here with the if condition.

if df(x1) ~= 0
    for i=1:1000
        x2=x1-(f(x1)/df(x1));  
        if abs (f(x2)) < TOL
            break
        end
        x1=x2;
    end
end
L=2*pi*h/x1;
% PLOT
kgel=x1/h;
xi=-L/4;
xf=5*L/4; 
t=0;
fplot(@(x) H/2 * cos(kgel.*x - w*t),[xi xf],'Color','c','LineWidth',1.5)
title('u and w in t=0')
xlabel('x axis')
ylabel('z axis')
grid

nx1=L/4;
nx2=3*L/4;
nx3=L/2;
nx4=L;
%x-velocity
u = @(z) (H*w/2)*(cosh(kgel*(h+z))/sinh(kgel*h))*cos(kgel*nx1-w*t);
%y-velocity
v = @(z) (H*w/2)*(sinh(kgel*(h+z))/sinh(kgel*h))*sin(kgel*nx1-w*t);
figure
fplot(u,[-h H])

figure
fplot(v,[-h H])