poisson1D(f,Uleft,U​right,N,L)

Solves 1D poisson equation, with dirichlet boundary conditions using SINE transform

function out = poisson1D(f,Uleft,Uright,N,L)
% POISSON1D solves the poisson equation d2U/dX2 = F.
% u = poisson1D(f,Uleft,Uright,N,L)
%
% f: a vector representing the right-hand-side
% Uleft: dirichlet boundary condition at u(0)
% Uright: dirichlet boundary condition at u(L)
% N: Number of nodes
% L: Length of domain
dx = L / (N - 1);
uB = zeros(length(f),1);
uB(2) = Uleft;
uB(end-1) = Uright;
f = f * dx^2 - uB;
b = dst(f);
m = (1:length(b))';
a = b ./ (2 * ( cos(m * pi / (N - 1)) - 1 ));
uSOL = idst(a);
uSOL(1) = Uleft;
uSOL(end) = Uright;
out = uSOL;
end