Combined Compact Symplectic Schemes for Solving Good Boussinesq Equations

Zhenyu Lang; Xiuling Yin; Yanqin Liu; Zhiguo Chen; Shuxia Kong

doi:10.20944/preprints202406.1509.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 20 June 2024 / Approved: 21 June 2024 / Online: 21 June 2024 (10:48:17 CEST)

Good Boussinesq equations will be 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 symplectic scheme in time direction, which are sympletic-structure preserving.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 test indicate that the fully discrete schemes are efficient in solving the spatial derivative mixed equation.

Hamiltonian system; good Boussinesq equation; symplectic scheme; combined compact scheme; conservation

Computer Science and Mathematics, Computational Mathematics

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Combined Compact Symplectic Schemes for Solving Good Boussinesq Equations

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