function udot=ex5_ode(t,u)
% udot=ex5_ode(t,u)
% heat equation, finite differences, uniform mesh, no generation term
% k=2*x+t+1
% x in [0,1], t>0

% mms $Id: $

N=100;
uleft=0;
uright=0;
dx=1/N;
x=(1:N-1)*dx;

% error checking
if length(u) ~= N-1
  error('ex5_ode: length(u) is wrong.');
end

dx=1/N;
for n=1:N-1
  kright=(2*(x(n)+dx/2)+t);
  kleft =(2*(x(n)-dx/2)+t);
  if n==1  %left
    udot(n,1)=(kright*(u(n+1)-u(n))-kleft*(u(n)-uleft ))/dx^2;
  elseif n<N-1  %interior
    udot(n,1)=(kright*(u(n+1)-u(n))-kleft*(u(n)-u(n-1)))/dx^2;
  else %right
    udot(n,1)=(kright*(uright-u(n))-kleft*(u(n)-u(n-1)))/dx^2;
  end
end