How to plot a 2 variables function with integration and sum

Hello, I would like to plot:

With :

I tried to break it down between the operations of integration and series sum.

% f1 = sin(n.*y.*pi);
% f2 = int(f1,y,0,L); or trapz(y, f1meshgrid,1); 
% f3 = f2* exp(n.*t.*pi)*sin(n.*y.*pi);
% f4 = cumsum or symsum (f3,dimN)

L = 0.01;
NbPts = 10; 
y = linspace(0,L,NbPts);
t = linspace(0,30,NbPts);
n = 0:1:NbPts;

f1 = @(n,y)sin(n.*y.*pi/L);
[N,Y] = meshgrid(n,y); 
f1mtn = f1(N,Y);
f2 = trapz(n, f1mtn,2); 
f3 = @(n,y,t) f2*exp(n.*t.*pi)*sin(n.*y.*pi);
[N2,Y2,T2] = meshgrid(n,y,t);
f3mtn = f3(N2,Y2,T2);
f4 = @(y,t) cumsum(f3mtn,3);
[Y3,T3] = meshgrid(y,t);
f4mty = f4(Y3,T3);
figure();
surfc(Y3,T,f4mty);

I obtain the error when I do f3mtn = f3(N2,Y2,T2) :

Error using  * Inputs must be 2-D, or at least one input must be scalar. To compute elementwise TIMES, use TIMES (.*) instead.

But I have 3 variables and I don't see how I can reduce them. Any suggestion to code this? Many thanks.

Answer 1

[darova]

clc, clear

L = 15;
NbPts = 50; 
y = linspace(0,L,NbPts*3);
t = linspace(0,0.1,NbPts);
n = 1:2:NbPts;

[N1, Y1] = meshgrid(n,y);
cn = trapz(y, sin(pi*N1.*Y1/L) );
plot(cn)

[T2, Y2, Cn] = meshgrid(t,y,cn);
[~, ~, N2] = meshgrid(t,y,n);

k = N2*pi./L;
u = Cn.*exp(k.*T2).*sin(k.*Y2);
U = sum(u,3);
[T3,Y3] = meshgrid(t,y);
figure
surf(T3,Y3,U)
xlabel('Time axis')
ylabel('Y xis')

[Hellema Ibrahim]

Thank you very much Darova. Would you mind to explain why the magical 2 lines:

[T2, Y2, Cn] = meshgrid(t,y,cn);
[~, ~, N2] = meshgrid(t,y,n);

I don't understand why we have to create a new vector Cn and new vector N2. Could you also clarify why we need 3 times more NbPts for y?

Thank you in advance.

[darova]

We need to have all matrix the same dimension (3D). You can't multiply 1D x 3D or 2D x 3D

f1mtn = f1(N,Y);                                % matrix 2D
f2 = trapz(n, f1mtn,2);                         % Vector 
f3 = @(n,y,t) f2*exp(n.*t.*pi)*sin(n.*y.*pi);
[N2,Y2,T2] = meshgrid(n,y,t);
% N2 - 3D matrix, Y2 - 3D matrix, T2 - 3D matrix
f3mtn = f3(N2,Y2,T2);                           % trying to multiply vector f2 by 3D

Maybe if you rewrite your code using loops it will be clearer. Two parts of the code below does the same

% [T2, Y2, Cn] = meshgrid(t,y,cn);
% [~, ~, N2] = meshgrid(t,y,n);
% k = N2*pi./L;
% u = Cn.*exp(k.*T2).*sin(k.*Y2);

u = zeros( length(t), length(y), length(cn) );
for i = 1:length(t)
    for j = 1:length(y)
        for k = 1:length(cn)
            k0 = n(k)*pi/L;
            u(i,j,k) = cn(k)*exp( k0*t(i) )*sin( k0*y(j) );
        end
    end
end
u = u';

Could you also clarify why we need 3 times more NbPts for y? - We dont. Size may be different

[Hellema Ibrahim]

Many thanks. Good day!