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Volume 13
Issue 9
10.3390/axioms13090574
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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations

by
Zhenyu Lang
1,
Xiuling Yin
2,*,
Yanqin Liu
2,
Zhiguo Chen
2 and
Shuxia Kong
2
1
School of Mathematics and Statistics, Shandong University of Technology, Zibo 255049, China
2
School of Mathematics and Big Data, Dezhou University, Dezhou 253023, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(9), 574; https://doi.org/10.3390/axioms13090574
Submission received: 19 June 2024 / Revised: 3 August 2024 / Accepted: 11 August 2024 / Published: 23 August 2024
(This article belongs to the Special Issue Advancements in Applied Mathematics and Computational Physics)
Versions Notes

Abstract

Good Boussinesq equations are considered in this work. First, we apply three combined compact schemes to approximate spatial derivatives of good Boussinesq equations. Then, three fully discrete schemes are developed based on a symplectic scheme in the time direction, which preserves the symplectic structure. Meanwhile, the convergence and conservation of the fully discrete schemes are analyzed. Finally, we present numerical experiments to confirm our theoretical analysis. Both our analysis and numerical tests indicate that the fully discrete schemes are efficient in solving the spatial derivative mixed equation.
Keywords: Hamiltonian system; good Boussinesq equation; symplectic scheme; combined compact scheme; conservation Hamiltonian system; good Boussinesq equation; symplectic scheme; combined compact scheme; conservation

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MDPI and ACS Style

Lang, Z.; Yin, X.; Liu, Y.; Chen, Z.; Kong, S. Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations. Axioms 2024, 13, 574. https://doi.org/10.3390/axioms13090574

AMA Style

Lang Z, Yin X, Liu Y, Chen Z, Kong S. Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations. Axioms. 2024; 13(9):574. https://doi.org/10.3390/axioms13090574

Chicago/Turabian Style

Lang, Zhenyu, Xiuling Yin, Yanqin Liu, Zhiguo Chen, and Shuxia Kong. 2024. "Combined Compact Symplectic Schemes for the Solution of Good Boussinesq Equations" Axioms 13, no. 9: 574. https://doi.org/10.3390/axioms13090574

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