In this paper, by applying the Faedo-Galerkin approximation method and using basic concepts of nonlinear analysis, we study the initial-boundary value problem for a nonlinear pseudoparabolic equation with Robin–Dirichlet conditions. It consists of two main parts. Part 1 is devoted to proof of the unique existence of a weak solution by establishing an approximate sequence
u
m
based on a
N
-order iterative scheme in case of
f
∈
C
N
0,1
×
0
,
T
∗
×
ℝ
N
≥
2
, or a single-iterative scheme in case of
f
∈
C
1
Ω
¯
×
0
,
T
∗
×
ℝ
. In Part 2, we begin with the construction of a difference scheme to approximate
u
m
of the
N
-order iterative scheme, with
N
=
2
. Next, we present numerical results in detail to show that the convergence rate of the 2-order iterative scheme is faster than that of the single-iterative scheme.