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arXiv · 1911.10845

Structure-preserving algorithms for multi-dimensional fractional Klein-Gordon-Schr\"{o}dinger equation

Yayun Fu Wenjun Cai·Yushun Wang
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Abstract

This paper aims to construct structure-preserving numerical schemes for multi-dimensional space fractional Klein-Gordon-Schr\"{o}dinger equation, which are based on the newly developed partitioned averaged vector field methods. First, we derive an equivalent equation, and reformulate the equation as a canonical Hamiltonian system by virtue of the variational derivative of the functional with fractional Laplacian. Then, we develop a semi-discrete conservative scheme via using the Fourier pseudo-spectral method to discrete the equation in space direction. Further applying the partitioned averaged vector field methods on the temporal direction gives a class of fully-discrete schemes that can preserve the mass and energy exactly. Numerical examples are provided to confirm our theoretical analysis results at last.

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Yayun Fu Wenjun Cai, Yushun Wang. 2019-11-25. Structure-preserving algorithms for multi-dimensional fractional Klein-Gordon-Schr\"{o}dinger equation. https://arxiv.org/abs/1911.10845

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