In this paper we study the numerical solution of nonlinear Volterra integro-differential equations with infinite delay by spline collocation and related Runge-Kutta type methods. The kernel function in these equations is of the form
k
(
t
,
s
,
y
(
t
)
,
y
(
s
)
)
k(t,s,y(t),y(s))
, with a representative example given by Volterra’s population equation, where we have
k
(
t
,
s
,
y
(
t
)
,
y
(
s
)
)
=
a
(
t
−
s
)
⋅
G
(
y
(
t
)
,
y
(
s
)
)
k(t,s,y(t),y(s)) = a(t - s) \cdot G(y(t),y(s))
.