T(x,y,afa) is a generated integrand, and the codes are as following.When I calculate M=arrayfun(@(D) integral2(@(x,y) T(x, y, D), 0,pi/2,-pi/6,pi/6,'reltol', 1e-6), afa) with varying afa=0:0.005:pi/6, the curve of output is not smooth and seems like noise. This is because the integrand has singular points. How to solve this problem? Many thanks!
function U=T(x,y,afa)
d1=1.34e-9;
d2=1.34e-9;
mu=5.5;
vh=1;
HBAR=1.05457266e-34;
ME=9.1093897e-31;
ELEC=1.60217733e-19;
Kh=2.95e10;
kc=sqrt(2.*ME.*ELEC./HBAR.^2);
k=kc.*sqrt(mu);
kh=sqrt(k.^2-(Kh-k.*sin(x).*cos(y)).^2-k.^2.*sin(x).^2.*sin(y).^2);
khg=sqrt(k.^2-(2.*Kh.*sin(afa./2).*sin(afa./2)-k.*sin(x).*cos(y)).^2-(2.*Kh.*sin(afa./2).*cos(afa./2)+k.*sin(x).*sin(y)).^2);
khpl=sqrt(k.^2-(Kh-k.*sin(x).*cos(y)).^2-k.^2.*sin(x).^2.*sin(y).^2+kc.^2.*vh);
khplpl=sqrt(k.^2-(Kh-k.*sin(x).*cos(y)).^2-k.^2.*sin(x).^2.*sin(y).^2+2.*kc.^2.*vh);
khgplpl=sqrt(k.^2-(2.*Kh.*sin(afa./2).*sin(afa./2)-k.*sin(x).*cos(y)).^2-(2.*Kh.*sin(afa./2).*cos(afa./2)+k.*sin(x).*sin(y)).^2+2.*kc.^2.*vh);
A2=exp(i.*khpl.*d1)./(exp(i.*(kh+khgplpl-khg).*d1)+exp(i.*khplpl.*d1));
U=abs(A2).^2;
end
