1u.m

用差分法解一类Bessel方程在不同边界条件下的离散解

a=33,R=135,u=[30,40,50,70,80,100];
 for i=1:6
    title('bessel函数在u变化时的情形')
    xlabel('自变量X')
    ylabel('函数值Y')
    b=1-a;
    t=sqrt(u(i));
    Q=60;
	B=besselj(1,t*R)*Q/(besselj(1,t*R)*(a*bessely(0,t)-b*t*bessely(1,t))-bessely(1,t*R)*(a*besselj(0,t)-b*t*besselj(1,t)));
	A=bessely(1,t*R)*Q/(besselj(1,t*R)*(a*bessely(0,t)-b*t*bessely(1,t))-bessely(1,t*R)*(a*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 ('u=30','u=40','u=50','u=70','u=80','u=100',0)