A-alpha stable - how to calculate alpha
4 views (last 30 days)
Show older comments
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')|
Thank you for any input!
0 Comments
Answers (0)
See Also
Categories
Find more on FPGA, ASIC, and SoC Development in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!