Error using vertcat-Dimensions of matrices being concatenated are not consistent - matlab

Question

I'm new to Matlab and am trying to implement this scheme.
Scheme: Un+1 = Minv*((1+2theta)*Un + *Un-1 +bn+1 + fn+1
Given the following equation:
ut(x; t) = cuxx(x; t) + f(x; t)
where x belongs to ]0; 1[: t belongs to ]0; T[, T > 0 and c>0
with Dirichlet boundaries
conditions:
u(0; t) = alpha(t)
u(1; t) = beta(t)
t belongs to [0; T]
The goal of the function in the code is to determine the error(defined in the code).
I keep getting:
Error using vertcat
Dimensions of matrices being concatenated are not consistent.
Error in wave1d_func11910448 (line 60)
uh=[UL;U;UR];
The code:
function [ h,err ] = wave1d_func11910448( nx )
a=0.0; b=1.0;
nx=20;
c=1.0;
tfinal=1;
h=(b-a)/(nx-1);
dt=0.5*h*h/c;
lambda=c*dt/h/h;
theta=1;
x=linspace(a,b,nx);
%defining the function f(x,t)
f = #(x,t) (pi^2-1)*exp(-t)*cos(pi*x)+4*x-2;
Fh=zeros(nx-2,1);%filling the vector f(n+1)
%defining the function g(x,t):initial condition-filling the vector U0
u = #(x) x.^2+cos(pi*x);
U0=u(x(2:end-1));
%defining the exact solution exact(x,t)
exact=#(x,t) x.^2+4*x*t+cos(pi*x)*exp(-t);
%filling the vector u1
U1=exact(x(2:end-1),1);
%defining the functions alpha(t) and beta(t)
alpha = #(t) exp(-t);
beta = #(t) -exp(-t)+4*t+1;
%filling the matrix Mh
Ah=diag(0.0*ones(1,nx-2),0)+diag(1.0*ones(1,nx-3),1)+diag(1.0*ones(1,nx-
3),-1);
Mh=eye(nx-2,nx-2)*(1+theta+2*lambda)-lambda*Ah;
Minv=inv(Mh);
Bh = zeros(nx-2,1);%filling the vector b
time=0.0;
i=0.0;
U2=Minv.*((1+2*theta )*U1-theta*U0+Bh+ dt*Fh);
while(time<tfinal)
time=time+dt;
i=i+1;
Bh(1)=lambda*alpha(time);Bh(nx-2)=lambda*beta(time);
Fh=f(x(2:end-1),time);
U=Minv.*((1+2*theta )*U1-theta*U0+Bh+ dt*Fh);
U0=U1;
U1=U2;
UL=alpha(time);
UR=beta(time);
uh=[UL;U;UR];
error(i) = norm(uh - exact(x,time),inf);
end
err=max(error);
expected results: err= a positive number <1
error message:
Error using vertcat
Dimensions of matrices being concatenated are not consistent.
Error in wave1d_func11910448 (line 60)
uh=[UL;U;UR];