求解Boussinesq方程的四阶紧致隐式显式Runge-Kutta格式

doi:10.3969/j.issn.1005-3085.2025.04.007

Chinese Journal of Engineering Mathematics

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A Fourth-order Compact Implicit Explicit Runge-Kutta Scheme for Boussinesq Equation

WANG Hongyu^1,2, Elminur Nizam¹, Kaysar Rahman¹

1. College of Mathematics and System Science, Xinjiang University, Urumqi 830017
2. College of Health Management Modern Industry, Jinzhou Medical University, Jinzhou 121001

Received:2022-11-05 Accepted:2023-04-27 Online:2025-10-15 Published:2025-10-15
Contact: Kaysar Rahman E-mail address: kaysar2014@sina.com
Supported by:
The Natural Science Foundation of Xinjiang Uygur Autonomous Region (2024D01C43); the Doctoral Startup Fund of Xinjiang University (BS150204).

Abstract

Abstract:

In this paper, a compact difference scheme which is fourth-order in space and third-order in time for the Boussinesq equation is proposed by using the three-point fourth-order compact finite difference method in space and the third-order strong-stability-preserving implicit and explicit Runge-Kutta method (SSP-IMEXRK3) in time.~The stability of the proposed scheme is verified by Fourier analysis. Based on several numerical examples, the result analysis and comparisons with other schemes verify the effectiveness of the proposed scheme.

Key words: Boussinesq equation, fourth-order compact difference scheme, implicit-explicit Runge-Kutta method

CLC Number:

O241.82

WANG Hongyu, Elminur Nizam, Kaysar Rahman. A Fourth-order Compact Implicit Explicit Runge-Kutta Scheme for Boussinesq Equation[J]. Chinese Journal of Engineering Mathematics, doi: 10.3969/j.issn.1005-3085.2025.04.007.

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A Fourth-order Compact Implicit Explicit Runge-Kutta Scheme for Boussinesq Equation

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