bessl3q.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

clear;
Q=[-5,-1,0,1,2,6],a=2,u=1,R=6;
w=sqrt(u);
for i=1:6
    b=1-a;
    A=Q(i)/(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(i)/(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));
    x=-6:0.1:6;
    y=A*besseli(0,w*x)+B*besselk(0,w*x);
   switch i
        case 1,
            plot(x,y,'k');
        case 2,
            plot(x,y,' . k');
        case 3,
            plot(x,y,' > k');
        case 4,
            plot(x,y,' * k');
        case 5,
            plot(x,y,' < k');
        case 6,
            plot(x,y,' -- k');
        end;
        hold on;
    end;
    hold off;
    axis([-6 6 -1 1]);
    legend('Q= -5','Q= -1','Q= 0','Q=1','Q= 2','Q=6',0)
    title('第三种边界条件下不同Q值的图象','FontSize',12,'FontName','隶书');