How do I make two waves move simultaneously towards each other to see the change in amplitude?

a = -20;
b = 20;
n = 1000;
T = 10;
zeta = @(x) 1;
alpha = @(x) 1.5*exp(-10*x.^2);
beta = @(x) 1.5*exp(-0.25*(x-10).^2);

delta = (b - a)/n;
m = floor(T/delta);

for j = 1:n+1
    x(j) = a + (j - 1)*delta;
end

for k = 1:m+1
    t(k) = (k - 1)*delta;
end

for j = 1:n
    r(j) = (zeta(x(j)) - zeta(x(j+1)))/(zeta(x(j)) + zeta(x(j+1)));
end

for j = 1:n+1
    v(1,2*j-1) = alpha(x(j));
    v(1,2*j) = beta(x(j));
    u_approx(1,j) = v(1,2*j-1) + v(1,2*j);
end

for k = 2:m+1
    v(k,1) = alpha(x(1) - t(k));
    v(k,2*n+2) = beta(x(n+1) + t(k));
end

for k = 1:m
    for j = 2:n+1
        v(k+1,2*j-1) = (1 + r(j-1))*v(k,2*j-3) - r(j-1)*v(k,2*j);
    end
end

for k = 1:m
    for j = 1:n
        v(k+1,2*j) = r(j)*v(k,2*j-1) + (1 - r(j))*v(k,2*j+2);
    end
end

for k = 1:m
    for j = 1:n+1
        u_approx(k+1,j) = v(k+1,2*j-1) + v(k+1,2*j);
    end
end

for i = 1:8
    figure
    plot(u_approx(25*i,:))
end

I am trying to learn how to make a video where one curve is moving to the right, and the other curve is moving to the left. Thus, the two waves will eventually collide and separate with each other. I currently have them as separate plots where each wave moving left and right at certain times, but now, I basically want them to combine those plots together as a video.

u_approx is a m x n matrix, which makes it harder for me to learn how to work this out. I looked online but the animations mainly uses a function, when I am using a matrix. please help me.

Answer 1

[Roshni Garnayak]

You can use the 'pause' and 'hold' functions to create a dynamic plot. Refer to the following code to get an idea:

x = 1:1000;                 % Coordinates on x-axis
y1 = 1: 1000;               % Coordinates of y-axis of the first line
y2 = 1000:-1:1;             % Coordinates of y-axis of the second line

Y1 = y1(1);                    
Y2 = y2(1);
X = x(1);

for i = 1:1000
    X = [X, x(i+1)];
    Y1 = [Y1, y1(i+1)];
    Y2 = [Y2, y2(i+1)];
    plot(Y1, X)
    hold on
    plot(Y2, X)
    
    pause(0.1)
    axis([0 1000 0 1000]);
end

For more information about the 'pause' and 'hold' commands, refer to the following links:

https://www.mathworks.com/help/matlab/ref/pause.html

https://www.mathworks.com/help/matlab/ref/hold.html