Graph Amplitude vs Displacement at different times

I have a code created to solve 1D convection equation using finite difference approximation. I am able to get a graph where amplitude vs displacement is graphed at one time. How to I change the code so that I can plot amplitude vs displacement at multiple times, say (3 seconds, 6 seconds, 10 seconds, 30 seconds).

% solve 1D convection equation

clear

%Defined Parameters

Lmax = 10; % Maximum Length [meters]

Tmax= 3; % Maximum Time [seconds] (I chose the value)

c = 1; % constant wave speed [m/s]

%Parameters needed to solve the equation

imax = 1001; % number of space steps (x direction)

i = 0; % iteration counter

uint = 1; % initial displacement [m]

n = 0; % time iteration counter

%Courant Number

C = .8;

%change in x

dx = Lmax/(imax-1);

for i = 1:(Lmax/dx)+1

x(i) = dx*i;

end

dt = C*dx/c; %change in time calculation

%Initialize Conditions

t = 0; %time to zero

n = 0; %time counter

un = zeros(imax,1);

% Initial value of function u

imid = ((5.0/Lmax)*(imax-1))+1;

for i = 1:imid

un(i) = uint;

end

% Initial wave displacement

u0 = un;

% Boundary Conditions

unp1(1) = uint;

unp1(imax) = 0;

while (t < Tmax) % loop for when time less than maximum time

n = n + 1;

t = t + dt; % increment time

%unp1 = un;

% Value of amplitude at the boundary at any time

for i=2:imax-1

unp1(i) = un(i) - .5*C*(un(i+1)-un(i-1)); %CASE A

% unp1(i) = un(i) - C*(un(i)-un(i-1)); %CASE B

%unp1(i) = un(i) - .5*C*(3*un(i)-4*un(i-1)+un(i)); %CASE C

end

%solve unp1 at every grid

un = unp1;

end

% Graphical Representation Function

plot (x, u0, "-m", x, unp1, "-k"); %colors magenta and black

xlabel('Wave Displacement (m)');

ylabel('Amplitude (m)');

axis ([0 10 0 2]);

title('Amplitude vs. Wave Displacement at Different Times');

[Maria]

I don't understand the question. Your code plots the following:

By different times, do yo mean plotting different waves? As in the magenta and black? Please explain a bit further. Thanks.

[Lindsay Mau]

Yes plotting different waves on the same graph. The different waves would be from responses at different times.

Answer 1

[Maria]

You need to storage the different responses for each Tmax in different arrays and the use the command "hold on" and plot all of them on the same figure. You could try and make a for loop where you vary Tmax on each iteration, and store the 'unp' values of each iteration in a matrix, as: [unp(t1), unp(t2), unp(t3)]. Then you could just plot all the different signals on one figure.