论文标题
非线性schrödinger方程的标量辅助变量方法的收敛，错误分析和长期行为
Convergence, error analysis and longtime behavior of the Scalar Auxiliary Variable method for the nonlinear Schrödinger equation
论文作者
论文摘要
我们对应用于非线性Schrödinger方程的标量辅助变量（SAV）方法进行了收敛分析，该方法在离散级别上保留了修改的哈密顿量。我们得出弱且强大的收敛结果，建立二阶全局误差界限，并对修改后的哈密顿式估计进行长时间误差估计。此外，我们说明了与某些应用中的经典拆分方案相比，SAV方法的有利能源保护。
We carry out the convergence analysis of the Scalar Auxiliary Variable (SAV) method applied to the nonlinear Schrödinger equation which preserves a modified Hamiltonian on the discrete level. We derive a weak and strong convergence result, establish second-order global error bounds and present long time error estimates on the modified Hamiltonian. In addition, we illustrate the favorable energy conservation of the SAV method compared to classical splitting schemes in certain applications.
