bessl4in1.m

主要阐述的是使用差分法解一类Bessel方程在不同边界条件下的离散解

Q=-5,a=0.2,R=2,u=1;
b=1-a;
w=sqrt(u);
A=0;
B=Q/(a*besselk(0,w)-b*w*besselk(1,w));
x=-2:0.05:2;
y=A*besseli(0,w*x)+B*besselk(0,w*x);
plot(x,y,' . k');
hold on;
A=Q/(a*besseli(0,w)+a*besselk(0,w)*(besseli(1,w*R)/besseli(1,w*R))+b*w*besselk(1,w)-b*w*besseli(1,w)*(besseli(1,w*R)/besselk(1,w*R)));
B=Q/(a*besseli(0,w)*(besselk(1,w*R)/besseli(1,w*R))+a*besselk(0,w)+b*w*besseli(1,w)*(besselk(1,w*R)/besseli(1,w*R))-b*w*besselk(1,w));
y=A*besseli(0,w*x)+B*besselk(0,w*x);
plot(x,y,' * k');
A=Q/(a*besseli(0,w)-a*besselk(0,w)*(besseli(0,w*R)/besselk(0,w*R))+b*w*besseli(1,w)+b*w*besselk(1,w)*(besseli(0,w*R)/besselk(0,w*R)));
B=Q/(a*besselk(0,w)-a*besseli(0,w)*(besselk(0,w*R)/besseli(0,w*R))-b*w*besseli(1,w)*(besselk(0,w*R)/besseli(0,w*R))-b*w*besselk(1,w));
y=A*besseli(0,w*x)+B*besselk(0,w*x);
plot(x,y,'k');
hold off;
legend('第一右边界','第二右边界','第三右边界',0);
title('Q=-5 a=0.2 R=2','FontSize',12,'FontName','隶书');
hold off