Why cumtrapz does not give same results as my analytic solution?

I wanted to test a numerical integration routine and used the following test function:

x=linspace(-10,10,100);
xs=x/30;
y=besselj(0,xs.*x).*x;
Yan=besselj(1,xs.*x(end)).*x(end)./xs;
Ynum=cumtrapz(x,y);


hold on 
plot(xs,abs(Yan).^2,'b')
plot(xs,abs(Ynum).^2,'--r')
legend('Analytic result','Numeric result');
grid on
hold off

Unfortunately my results are not the same. I hope someone could give an explanation why they are not the same, my guess there is some scaling that goes wrong.

Answer 1

[darova]

I think it happens because of limits of integration

x = linspace(-2,3);
y = x.^2;
c0 = x(1)^3/3;
plot(x,cumtrapz(x,y),'.-r')
line(x,x.^3/3-c0)           % try without c0

[Romano Groeneveld]

But how would i obtain the right results if i have to solve something numerical without having the analytic solution?

Like even if I use something simple as cosine, it seems to go wrong with cumtrapz:

clear;close all;clc;

N=300;
vv=linspace(1,4,N);
ss=linspace(0,2*pi,N);


for i=1:length(vv)
    v=vv(i);
    I(i)=integral(@(r) cos(v.*r),0,2*pi,'ArrayValued',1);
end

fun=cos(vv.*ss);
Inum=cumtrapz(ss,fun);

hold on
plot(ss,I,'b');
plot(ss,Inum,'r');
hold off
grid on
xlim([0 2*pi]);

[darova]

Try to check calculated curves using diff

[darova]

Did you find out what was wrong?