give me invalid use of operator at U, why?

Nx = 50;
x = linspace(0,1,Nx+1);
dx = 1/Nx;
xmid = 0.5*(x(1:Nx) + x(2:Nx+1));
u = 1;
tfinal = 1;
CFL = 0.5;
dt = CFL*dx/abs(u);
U = 0.75*exp(-((xmid-0.5)/0.1). 2)';
t = 0;
% Loop until t > tfinal
while (t < tfinal),
    Ubc = [U(Nx); U; U(1)]; % This enforces the periodic bc
    % Calculate the flux at each interface
    F = 0.5* u *( Ubc(2:Nx+2) + Ubc(1:Nx+1)) ...
        - 0.5*abs(u)*( Ubc(2:Nx+2) - Ubc(1:Nx+1));
    % Calculate residual in each cell
    R = F(2:Nx+1) - F(1:Nx);
    % Forward Euler step
    U = U - (dt/dx)*R;
    % Increment time
    50 t = t + dt;
    % Plot current solution
    stairs(x,[U; U(Nx)]);
    axis([0, 1, -0.5, 1.5]);
    grid on;
    drawnow;
end
% overlay exact solution
U = 0.75*exp(-((xmid-0.5)/0.1).ˆ2)';
hold on;
stairs(x,[U; U(Nx)], 'r-');

Answer 1

[Walter Roberson]

U = 0.75*exp(-((xmid-0.5)/0.1). 2)';

my guess is that you wanted

U = 0.75*exp(-((xmid-0.5)/0.1).^2)';