function [E,F,W]=tridiag(A,B,C,D,M,E1,F1,WM)
%
% TRIDIAG a function file to solve the tridiagonal matrix problem
%	taken from Roache, Appendix A. Notation in this file is
%	consistant with that in Roache.
%
% SYNTAX:
%	[E,F,W]=tridiag(A,B,C,D,M,E1,F1,WM)
%
% INPUT:
%	A = the first coefficient of the interior-point formulation
%	B = the second coefficient
%	C = the third coefficient
% 	D = the fourth coefficient
%	M = the number of spatial grid points
%	E1 = the first coefficient from the left-hand BC
%	F1 = the second coefficient from the left-hand BC
%	WM = the right-hand BC
% OUTPUT:
%	E = the first internal coefficient
%	F = the second internal coefficient
%	W = the dependent variable solution
%
% Typically all differential equations solvable by this method can be
%	written in the interior-point form:
%
%		-AmWm+BmWm-CmWm=Dm
%	where:
%		m=spatial index (m=1,2,...,M-1)
%
% This is done by assuming two additional vectors can be created such
%	that:
%
%		Wm=EmW(m-1)+Fm
%
%	can be solved recursively
%
% Started 96:10:31 D.M. Glover

E=zeros(1,M-1);
F=zeros(1,M-1);
W=zeros(1,M);
E(1)=E1;
F(1)=F1;

for j=2:M-1
   E(j)=A(j)/(B(j)-C(j)*E(j-1));
   F(j)=(D(j)+C(j)*F(j-1))/(B(j)-C(j)*E(j-1));
end

W(M)=WM;

for j=(M-1):-1:1
   W(j)=E(j)*W(j+1)+F(j);
end