A-alpha stable - how to calculate alpha

4 次查看（过去 30 天）

ivordes greenleaf 2016-3-2

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/270952-a-alpha-stable-how-to-calculate-alpha

So I have some made up BDF scheme, and I was able to plot out the boundary of the abs stability region. I can see that BDF#3 and BDF#4 is not A stable, but in face, A-alpha stable. Is there any way to write a code so that would calculate the measurement of alpha? I saw the measurement of alpha reported in different paper (for example, the original BDF3 iw A-86 degree stable), but how does one calculate that?

I include that coding I have:

clc;
x=linspace(-20,20,1000);
y=linspace(-20,20,1000);
theta=0:0.001:2*pi;
Z=exp(i*theta);
%Euler's Method
M=Z-1;
plot(real(M),imag(M),'g');
hold on
grid on
%BDF#1
M=(Z-1)./(Z);
plot(real(M),imag(M),'r','linewidth',2);
%BDF#2
M=((3/2).*(Z.^2)-2.*Z+0.5)./(Z.^2);
plot(real(M),imag(M),'k','linewidth',2);
axis equal
%M=(Z.^2-(4/3)*Z+(1/3))./((2/3)*Z.^2)
%plot(real(M),imag(M),'b');
%BDF#3
M=((11/6)*Z.^3-3*Z.^2+1.5*Z-(1/3))./(Z.^3);
plot(real(M),imag(M),'c','linewidth',3);
%BDF#4
M=((25/12)*Z.^4-4*Z.^3+3*Z.^2-(4/3)*Z+0.25)./(Z.^4);
plot(real(M),imag(M),'m','linewidth',2);
legend('Eulers Method','BDF#1','BDF#2','BDF#3','BDF#4')|