Image:Stability region for AB2 method.png

[edit] Summary

[edit] Licensing

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[edit] Matlab code

clf;
[X,Y] = meshgrid(linspace(-3,2), linspace(-2,2));
Z = X+Y*1i;
phi1 = 1/2 * (1 + 3/2*Z + sqrt(1+Z+9/4*Z.^2));
phi2 = 1/2 * (1 + 3/2*Z - sqrt(1+Z+9/4*Z.^2));
contourf(X,Y,1-max(abs(phi1),abs(phi2)), [0 0], 'LineWidth', 1);
set(gca, 'FontSize', 20, 'CLim', [0 1]);
colormap([1 .5 .8; 0 0 0]);
hold on;
plot([-3 2], [0 0], '--k', 'LineWidth', 1);
plot([0 0], [-2 2], '--k', 'LineWidth', 1);
print -dpng 'ab2_lsd_tmp.png';
system('convert -trim -bordercolor white -border 10 +repage ab2_lsd_tmp.png ab2_lsd.png');

• Stiff equation