分数阶薛定谔方程的平均向量场方法

The average vector field method for fractional Schr dinger equation

基于二阶平均向量场方法和傅里叶谱方法构造了分数阶薛定谔方程的哈密尔顿保结构格式,并利用新格式数值模拟方程的演化行为.结果表明分数阶薛定谔方程的新格式具有二阶精度,且可以精确地保持方程的能量和质量守恒特性.

The Hamiltonian energy preserving scheme of fractional Schr dinger equation is constructed by the second-order average vector field method and Fourier spectral method.The evolution behavior of the equation is numerically simulated with the new scheme.The numerical results show that the new scheme of fractional Schr dinger equation has second-order accuracy and can preserve the energy and mass conservation property.