t = linspace ( 0.0, 2.0 * pi, 101 );
z = ( exp ( 2 * i * t ) - exp ( i * t ) ) ./ ( 1.5 * exp ( i * t ) - 0.5 );
xmin = min ( real ( z ) );
xmax = max ( real ( z ) );
ymin = min ( imag ( z ) );
ymax = max ( imag ( z ) );
clf ( );
hold ( 'on' );
plot ( real ( z ), imag ( z ), 'linewidth', 3 );
plot ( [ 0.0, 0.0 ], [ymin,ymax], 'k-' );
plot ( [xmin,xmax], [0.0,0.0], 'k-' );
hold ( 'off' );
axis ( 'equal' );
title ( 'Stability boundary for AB2 ODE solver' );
print ( '-dpng', 'border_plot.png' );
