Matlab command window showing error and no working fine

function Final_difference

clear clc close all format long

% Constant coefficient alpha = 1; beta = 1;

% Boundary condition l = 0; L = 1;

N = 50; x = linspace(l,L,N);% spial dx = x(2)-x(1);

% Timespan & Initial condition tf = 8; ns = 20; tspan = linspace(0,tf,ns);

U0 = 1; U_in = U0*ones(N,1); % at t=0 figure (1);

[t,s] = ode15s(@oden,tspan,U_in);

% Another way for ploting, haven't figured it out whether to use it or not % Usol = s(:,1:N); % Usol(10,end) % figure(1); % box on % hold on % subplot(2, 1, 1) % plot([x], [Usol(1:10:ns,:)],'b'); % xlabel ('space x'); % ylabel('U');

plot(t,s(:,1)) title('The solution of Heat equation') xlabel('time t') ylabel('concentration U')

%ODE15s function function F = oden(t,ys) % F is same as dudt, U = ys(1:N,1); % F(1,1)=(1/dx^2)*(2*U(2)-2*U(1))+alpha*(2*U(2))./2*dx % F(3,1) = beta*((U(4)-2*U(3)+U(2))/dx)/dx+alpha*((U(4)-U(2))./(2*dx)) F(2:N-1,1) = (beta*(((U(3:N)-2*U(2:N-1)+U(1:N-2))/dx)/dx))+(alpha*(U(3:N)-U(1:N-2))./(2*dx)) % F(N,1)=(1/dx^2)*(U(N+1)-2*U(N)+U(N-1))+alpha*(U(N+1)-U(N-1))./2*dx end end

Just update something, it gets better but still not working properly.

This is what the command window is showing. Error using odearguments (line 92) FINAL/ODEN returns a vector of length 49, but the length of initial conditions vector is 50. The vector returned by FINAL/ODEN and the initial conditions vector must have the same number of elements.

Error in ode15s (line 148) [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, odeFcn, ...

Error in Final (line 37) [t,s] = ode15s(@oden,tspan,U_in);