% mstepstab.m
%
% Written by: David Darmofal
%             February 20, 2003
%
% Purpose: plots the stability countour for multi-step methods
%

clear theta z g;

% Specify theta
theta = linspace(0,2*pi,301);

% Set growth factor
g = exp(i*theta);

% Calculate z-location 

% Adams-Bashforth 1 (i.e. Forward Euler)
z = g - 1;

% Adams-Moulton 1 (i.e. Backward Euler)
%z = (g-1)./g;

% Adams-Moulton 2 (i.e. Trapezoidal)
%z = (g-1)./(0.5*(g+1));

% Plot z-locus of g-contour
plot(z,'k-');
axis([-3,3,-3,3]);
axis('square');
xlabel('Real z');
ylabel('Imag z');
grid on;