1. The noise terms are defined as the identical terms with opposite signs
that may appear in the components u0(x)and u1(x) and in the other com-
ponents as well.
2. The noise terms appear only for specific types of inhomogeneous equa-
tions whereas noise terms do not appear for homogeneous equations.
3. Noise terms may appear if the exact solution of the equation is part of
the zeroth component u0(x).
4. Verification that the remaining non-canceled terms satisfy the integral
equation is necessary and essential.
The phenomenon of the useful noise terms will be explained by the follow-
ing illustrative examples.