Matrix Dimension doesn't agree: Please kindly help to review this code it keep saying matrix dimension must agree. Thanks.

% User Specified Information 

% Number of Fourier Modes
N = 16  ; 

% Temporal Domain and Stepsize
t0 = 0; tend = 10; dt = .01; 
t = (t0:dt:tend);

% Spatial grid (used in evaluation of exact solution)
x = (0:.01:1)';
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% Create Initial Fourier Coefficients - u(x,0) in fourier basis
n = (1:N)';
a(:,1)= -12*(-1).^n./(pi^3*n.^3);

[t, a] = ode45(@getRHS, t, a); a = a';

% Use numerical fourier coefficients to create numerical solution and
% create exact solution
u = zeros(numel(x),numel(t)); u0 = x-(x.^3); uexact(:,1) = u0; 
for(i=1:numel(t))
   for(n=1:N)
       % Exact Solution
       uexact(:,i+1) = uexact(:,i)+1 + (-12*(-1).^n)/(pi^3 * n.^3)*sin(n*pi*x)*exp(1-(n*pi)^2*t(i));
       % Numerical Solution 
       u(:,i) = u(:,i) + a(n,i)*sin(n*pi*x);
   end
   
   if(t(i) == 1)
       fprintf('u(.5,1) = %f. \n', u( (numel(x)-1)/2+1, i))
   end
   uexact(:,i) = uexact(:,i) + a(n,i)*sin(n*pi*x)*exp(1-(n*pi)^2*t(i)); 
end

size(u)
size(uexact)
size(x)
size(t)

% Visualization Requirement
figure(1), clf
mesh(t,x,abs(u-uexact))
xlabel('t')
ylabel('x')
zlabel('|u - uexact|')
title('Absolute Error in Spectral Projection Method')

       
    
end

function da = getRHS(t,a)

N = size(a); 

for(n=1:N)
   da(n,1) = -(n*pi)^2*a(n) + 1/pi*(1-(-1)^n)/n;
end

end

[Walter Roberson]

N = size(a);

is a a row or a column? because size with one input and one output always returns a vector and you are using that vector as a bound in for. You might know how it works today but by next week you will have forgotten. use numel instead of size

[Oluwaseun Farotimi]

Hey Walter,

I haved noted your correction.

Thanks.

Answer 1

[Ameer Hamza]

Change the call to mesh() like this

mesh(t,x,abs(u-uexact(:,1:end-1)))

[Oluwaseun Farotimi]

Hey Ameer,

It worked. Thank so much...

[Image Analyst]

Can you please "Accept this answer" to give Ameer credit (reputation points) and thanks for helping you? Thanks in advance.