The solution of the generalized Abel integral equation
\[
g
(
t
)
=
∫
0
t
{
k
(
t
,
s
)
/
(
t
−
s
)
α
}
f
(
s
)
d
s
,
0
>
α
>
1
,
g(t) = \int _0^t {\{ k(t,s)/{{(t - s)}^\alpha }\} f(s)} ds,\;0 > \alpha > 1,
\]
where
k
(
t
,
s
)
k(t,s)
is continuous, by the product integration analogue of the trapezoidal method is examined. It is shown that this method has order two convergence for
α
∈
[
α
1
,
1
)
\alpha \in [{\alpha _1},1)
with
α
1
≑
0.2117
{\alpha _1} \doteqdot 0.2117
. This interval contains the important case
α
=
1
2
\alpha = \tfrac {1}{2}
. Convergence of order two for
α
∈
(
0
,
α
1
)
\alpha \in (0,{\alpha _1})
is discussed and illustrated numerically. The possibility of constructing higher order methods is illustrated with an example.