% twoPointBvpDdirichletSpectral

   clear, home, close all
   
   N = 20;
  
   a = 0; b = 1;
 
   x = -cos(pi*((0:N-1)/(N-1)))';
   x = 0.5*(b-a).*x + 0.5*(b+a);    % maps [-1,1] to [a,b]
   
 
   dm = dmFirstFull(x,2);

     alpha = 0.2;       %  u (0) = alpha
      beta = 0.9;       %  u (1) = beta
      
     f = exp(x);
     
     uExact = exp(x) + x*(beta - exp(1) - alpha + 1) + (alpha - 1);
     
        dm(1,:) = 0;    dm(1,1) = 1;    f(1) = alpha;     %  Dirichlet BC at x = 0
        dm(N,:) = 0;    dm(N,N) = 1;  f(N) = beta;      %  Dirichlet BC at x = 1

      uApprox = dm\f;
     
      norm(uExact-uApprox,inf)
      plot(x,uApprox,'b--o',x,uExact,'r')