derlg

DERLG      Spectral (Legendre Gauss) derivative matrix 

    [d]=derlg(x,np) returns the spectral Legendre Gauss derivative
    matrix d at the np LG nodes X (in (-1,1)). np-1 is the polynomial
    degree used. Legendre Gauss (LG) grid


 Input: x = array of LG nodes on (-1,1) (computed by xwlg)
        np = number of LG nodes (=n+1, n=polynomial interpolation degree)

 Output: d = spectral derivative matrix

 Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
                    "Spectral Methods. Fundamentals in Single Domains"
                    Springer Verlag, Berlin Heidelberg New York, 2006.

0001 function [d] = derlg(x,np) 
0002 %DERLG      Spectral (Legendre Gauss) derivative matrix
0003 %
0004 %    [d]=derlg(x,np) returns the spectral Legendre Gauss derivative
0005 %    matrix d at the np LG nodes X (in (-1,1)). np-1 is the polynomial
0006 %    degree used. Legendre Gauss (LG) grid
0007 %
0008 %
0009 % Input: x = array of LG nodes on (-1,1) (computed by xwlg)
0010 %        np = number of LG nodes (=n+1, n=polynomial interpolation degree)
0011 %
0012 % Output: d = spectral derivative matrix
0013 %
0014 % Reference: CHQZ2 = C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang,
0015 %                    "Spectral Methods. Fundamentals in Single Domains"
0016 %                    Springer Verlag, Berlin Heidelberg New York, 2006.
0017 
0018 %   Written by Paola Gervasio
0019 %   $Date: 2007/04/01$
0020 
0021  
0022 n=np-1; 
0023 d=zeros(np);
0024  [p,pd] = jacobi_eval(x,np,0,0);
0025 for i=1:np
0026 for j=1:np
0027 if(i~=j)
0028     d(i,j)=pd(i,1)/(pd(j,1)*(x(i)-x(j)));
0029 elseif(i==j)
0030 d(i,j)=x(i)/(1-x(i)*x(i));
0031 end
0032 end
0033 end
0034  
0035 return