%
% accuracyPlotsAlgebraicConvergence
%  
%  first derivative
%
%  2nd and 4th order finite differences
%    and Chebyshev pseudospectral  

  clear, home, close all, format compact                     

%  Nvec = [10 20 20 40];

  Nvec = [20 40 80 160 320];

  for i = 1:length(Nvec)
  
        N = Nvec(i);
        h(i) = 2/(N-1);

            k = linspace(0,N,N)';
           xc = -cos(pi*k/N);
            x = -1 + (2/N).*k;
     
             u = exp(x);
            uc = exp(xc); 
            
            ue = exp(x);
            uce = exp(xc);
            
           dm2 = dmFirst3Pt(x); 
           dm4 = dmFirst5Pt(x); 
%           dmc = dmFirstFull(xc,1);
           
           uFd2 = dm2*u;
           uFd4 = dm4*u;
%           uCps = dmc*uc;
           
           e2(i) = norm(uFd2 - ue,inf);
           e4(i) = norm(uFd4 - ue,inf);
%           ec(i) = norm(uCps - uce,inf);

       if i>2
         rho2 = log(e2(i-1)/e2(i))/log(2)
         rho4 = log(e4(i-1)/e4(i))/log(2)
       end
      
  end
  
%  loglog(Nvec,e2,'b',Nvec,e4,'g',Nvec,ec,'r')

loglog(h,e2,'b',h,e4,'g')

%  loglog(h,e2,'b',h,e4,'g',h,ec,'r')
  

  title('Convergence of derivative approximations')