function A = nma_FDM_matrix_laplace_1D_robin(N,h,alpha)
% builds finite difference A matrix for 1-D laplace
%-----------------------------------------------------------------
% A = nma_FDM_matrix_laplace_1D_robin(N,h)
%
% returns the A matrix, which is the system finite difference matrix for
% numerical solution of 1-D laplace equation Uxx = f, with nuemman
% boundary conditions on both sides of the element. Based on 3 point
%
% INPUT: N, the number of nodes
% h, spacing between nodes
%
% OUTPUT: A, the matrix , see below
%
%
% A = A/h^2; % h is space between points
% U = A\f; % solve for U, where Uxx=f, need to set f as function before.
%
% copyright: Nasser M. Abbasi
% 10/18/2010
A = zeros(N);
for i=1:N
for j=1:N
% as before, part(a), Dirichlet B.C.
if(i==j)
A(i,j) = -2;
else
if( i==j+1 || i==j-1 )
A(i,j) = 1;
end
end
end
end
%fix A above
A(1,1) = -1-alpha*h;
end