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

TL;DR

This paper develops structure-preserving numerical schemes for multi-dimensional fractional Klein-Gordon-Schrödinger equations, ensuring exact conservation of mass and energy through novel semi-discrete and fully-discrete methods.

Contribution

It introduces a new class of structure-preserving algorithms based on partitioned averaged vector field methods for fractional PDEs, preserving key invariants.

Findings

Schemes exactly conserve mass and energy.

Numerical results confirm theoretical properties.

Methods effectively handle multi-dimensional fractional equations.

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.