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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.

A High-Order Iterative Scheme for a Nonlinear Pseudoparabolic Equation and Numerical Results