2a.m

用差分法解一类Bessel方程在不同边界条件下的离散解

a=[-10,-6,-4,0,6,10],u=40,R=13;
 for i=1:6
    title('bessel函数在a变化时的情形')
    xlabel('自变量X')
    ylabel('函数值Y')
    b=1-a(i);
	t=sqrt(u);
    Q=60;
	B=besselj(0,t*R)*Q/(besselj(0,t*R)*(a(i)*bessely(0,t)-b*t*bessely(1,t))-bessely(0,t*R)*(a(i)*besselj(0,t)-b*t*besselj(1,t)));
	A=bessely(0,t*R)*Q/(besselj(0,t*R)*(a(i)*bessely(0,t)-b*t*bessely(1,t))-bessely(0,t*R)*(a(i)*besselj(0,t)-b*t*besselj(1,t)));
	x=0:0.05:50;
	y=A*besselj(0,x)+B*bessely(0,x);
	switch i
		case 1,
			plot(x,y,'r-');
		case 2,
			plot(x,y,'g:');
		case 3,
			plot(x,y,'b-.');
        case 4,
			plot(x,y,'y-');
		case 5,
			plot(x,y,'m:');
		case 6,
			plot(x,y,'c-.');
    	end;
		hold on;
	end;
	hold off;
	legend ('a=-10','a=-6','a=-4','a=0','a=6','a=10',0);