Abstract
In this paper, a conservative compact finite difference scheme is presented to numerically solve the coupled Schrödinger-KdV equations. The analytic solutions of the coupled equations have some invariants such as the number of plasmons, the number of particles, and the energy of oscillations, and we proved that the compact difference scheme preserves those invariants in discrete sense. Optimal order convergence rate of the proposed linearized compact scheme was analyzed. Numerical experiments on model problems show that the scheme is of high accuracy.
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Acknowledgements
The authors would like to express their sincere gratitude to the reviewers for their valuable comments and suggestions on this paper.
Funding
The first author (Xie) was supported partially by the NNSF of China grants (11871443) and Fundamental Research Funds for the Central Universities (201562012), and the second author (Yi) was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2014R1A1A2055548, 2018R1D1A1B07041879).
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Communicated by: Aihui Zhou
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Xie, S., Yi, SC. A conservative compact finite difference scheme for the coupled Schrödinger-KdV equations. Adv Comput Math 46, 1 (2020). https://doi.org/10.1007/s10444-020-09758-2
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DOI: https://doi.org/10.1007/s10444-020-09758-2