It seems that Chebfun has issues to solve (nonlinear Volterra) integral equations on rather big domains

[Mike]

Hello my Chebfun friends!

The following code solves the nonlinear integral equation u(x) = int(0^t) K(x,t) * F(u(t)) dt where F(u) = u/(u+10)+10 and the kernel

K(x,t) = H(x-t), H(x)=exp(- int(0^x) mu(y) dy) and for this example I considered m(y)=y, for simplicity.

chebfunpref.setDefaults('splitting',true);

d=[0 40];

F=@(x)x./(x+10)+10;

mu=@(x)x;

syms x

H=matlabFunction(exp(int(-mu(x),0,x)));

K=@(x,t)H(x-t);

N=chebop(d);

N=chebop(@(x,u) -u+volt(K,F(u)),d);

u=N\0;

Actually, the above code does a good job! However, when I try to solve the same problem on a

bigger domain of d=[0 50] it, unfortunately, fails to solve the integral equation.

Any idea is GREATLY appreciated!

We had a crazy weather at Gronnigen today but I hope you had a good one at your place!

Best,

Babak 

[Nick Hale]

There was a small bug preventing this. I fixed it here:

https://github.com/chebfun/chebfun/pull/2362

I don't know why it's so slow. Probably using a symbolic 

function is not helping. Try to avoid that if possible.

N