Year: 2025
Type: article
Abstract: In this paper, we derive a semi-discrete scheme using the central difference method, which perfectly preserves the conservation of mass and energy for the Hirota equation. By applying the Crank–Nicolson method for temporal discretization, we develop the fully discrete scheme that conserves mass and energy. It is shown that the accuracy of the fully discrete scheme is of the second order in space and time. Because the Crank–Nicolson discretization leads to a nonlinear algebraic system, an efficient iterative solver is proposed that linearizes and solves the resulting five-diagonal matrix at each iteration while treating high-order contributions iteratively to reduce computational cost. Numerical experiments are presented to demonstrate the accuracy and verify the conservation properties.
Source: Mathematics
DOI: 10.3390/math13243899
Authors: Jinqi Zhang, Xianggui Li, Dongying Hua
Institution: Beijing Information Science & Technology University
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Award: G3784161081
OpenAlex ID: W4417045477