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

Nguyen Huu Nhan, Tran Trinh Manh Dung, Le Thi Mai Thanh, Le Thi Phuong Ngoc and Nguyen Thanh Long

Mathematical Problems in Engineering, 2021, vol. 2021, 1-17

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 based on a - order iterative scheme in case of , or a single-iterative scheme in case of . In Part 2, we begin with the construction of a difference scheme to approximate of the - order iterative scheme, with . 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.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:8886184

DOI: 10.1155/2021/8886184

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