求解耦合非线性Schrödinger-Boussinesq方程的三角标量辅助变量方法OACSTPCD
Trigonometric Scalar Auxiliary Variable Method for Coupled Nonlinear Schrödinger-Boussinesq Equation
采用三角标量辅助变量(TSAV)方法,构造求解耦合非线性Schrödinger-Boussinesq方程初边值问题的高效数值格式.基于方程非线性势能的三角函数形式,提出求解方程的TSAV格式;对方程在时间和空间上分别采用二阶Crank-Nicolson格式和傅里叶谱方法进行离散,并证明时间半离散格式的修正能量守恒律.最后,通过数值算例对文中格式进行验证.结果表明:文中格式具有有效性,修正能量具有守恒性.
Based on the trigonometric scalar auxiliary variable(TSAV)method,an efficient numerical scheme is con-structed to solve the initial boundary value problem of the coupled nonlinear Schrödinger-Boussinesq equation.Firstly,based on the trigonometric function form of the nonlinear potential energy equation,the TSAV scheme of the consid-ered equation is proposed.Then,the equation is discretized in temporal and spatial by using the second-order Crank-Nicolson scheme and Fourier spectral method respectively,and the modified energy conservation law of time semi-dis-crete scheme is proved.Finally,the proposed scheme is verified by numerical examples.The results show that the proposed scheme is effective and the modified energy is conserved.
郭姣姣;庄清渠
华侨大学数学科学学院,福建泉州 362021
数学
耦合非线性Schrödinger-Boussinesq方程三角标量辅助变量方法修正能量守恒律
coupled nonlinear Schrödinger-Boussinesq equationtrigonometric scalar auxiliary variable methodmodi-fied energyconservation law
《华侨大学学报（自然科学版）》 2024 (001)
98-107 / 10
国家自然科学基金资助项目(11771083);福建省自然科学基金资助项目(2021J01306)
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