function [ fval ] = F(t,x,u,ux,duxx)
% 
% Written by:
% -- 
% John L. Weatherwax                2005-06-15
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
  
fval(1) = duxx(1) - v(x)*ux(1); 

  


function [ vout ] = v(x)
% 
% Written by:
% -- 
% John L. Weatherwax                2005-06-15
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----
  
if( x >= 0 & x < 0.5 )
  vout(1) = 1000; 
elseif( x == 0.5 )
  xGrid200 = 0.49750; xGrid201 = 0.5; xGrid202 = 0.50500;
  vout(1) = ((xGrid201-xGrid200)*1.0 + (xGrid202 - xGrid201)*1000.0)/(xGrid202-xGrid200); 
else
  vout(1) = 1; 
end