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

Abstract

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.

Third Order Iterative Method for Solving Non-Linear Parabolic Partial Differential Equation in Financial Application

“…Therefore, due to this reason, several numerical methods have been developed for investigating the simulation of a nonlinear parabolic equation. For instance, in Nhan et al (2021), the high-order iterative scheme was used for the study of the non-linear pseudo-parabolic equation. They apply the Faedo-Galerkin approximation method and use basic concepts of non-linear analysis, but grid generation is usually more automatic for the Galerkin approximation method, although not completely for complex geometries.…”