A general conservative eighth-order compact finite difference scheme for the coupled Schrödinger-KdV equations

Jiadong Qiu; Danfu Han; Hao Zhou; Jiadong Qiu; Danfu Han; Hao Zhou

doi:10.3934/math.2023538

AIMS Mathematics

2023, Volume 8, Issue 5: 10596-10618. doi: 10.3934/math.2023538

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Research article

A general conservative eighth-order compact finite difference scheme for the coupled Schrödinger-KdV equations

School of Mathematics, Hangzhou Normal University, Hangzhou 310006, China

Received: 12 January 2023 Revised: 19 February 2023 Accepted: 23 February 2023 Published: 02 March 2023
MSC : 65M06, 65M12, 65M15

In this paper, we present a general conservative eighth-order compact finite difference scheme for solving the coupled Schrödinger-KdV equations numerically. The proposed scheme is decoupled and preserves several physical invariants in discrete sense. The matrices obtained in the eighth-order compact scheme are all circulant symmetric positive definite so that it can be used to solve other similar equations. Numerical experiments on model problems show the better performance of the scheme compared with other numerical schemes.
- Schrödinger-KdV equations,
- compact finite difference scheme,
- periodic boundary condition,
- conservation,
- error estimate
Citation: Jiadong Qiu, Danfu Han, Hao Zhou. A general conservative eighth-order compact finite difference scheme for the coupled Schrödinger-KdV equations[J]. AIMS Mathematics, 2023, 8(5): 10596-10618. doi: 10.3934/math.2023538

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Abstract

In this paper, we present a general conservative eighth-order compact finite difference scheme for solving the coupled Schrödinger-KdV equations numerically. The proposed scheme is decoupled and preserves several physical invariants in discrete sense. The matrices obtained in the eighth-order compact scheme are all circulant symmetric positive definite so that it can be used to solve other similar equations. Numerical experiments on model problems show the better performance of the scheme compared with other numerical schemes.

References

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