Riesz空间分数阶非线性sine-Gordon方程新的保能量格式

A new energy-preserving scheme for Riesz space fractional nonlinear sine-Gordon equation

首先利用傅里叶拟谱方法对Riesz空间分数阶导数离散近似,再利用Boole离散线积分方法结合高阶平均向量场方法构造出Riesz空间分数阶非线性sine-Gordon方程新的保能量格式。最后利用新格式数值模拟不同初值条件下Riesz空间分数阶非线性sine-Gordon方程孤立波的演化行为。数值实验验证了新格式的有效性和精确性。

In this paper a new energy-preserving scheme for Riesz space fractional nonlinear sine-Gordon equation is presented.The Riesz space fractional derivative was discretized initially by Fourier pseudo spectral method.Subsequently,a new energy-preserving scheme for Riesz space fractional nonlinear sine-Gordon equation was constructed by the Boole discrete line integral method and high order average vector field method.Finally,the new scheme was applied to numerically simulate the Riesz space fractional nonlinear sine-Gordon equation with different initial conditions.The validity and accuracy of the new scheme were verified by numerical experiments.