Error estimates of structure-preserving Fourier pseudospectral methods for the fractional Schrodinger equation
Error estimates of structure-preserving Fourier pseudospectral methods for the fractional Schrodinger equation
复制标题
分数阶薛定谔方程的保结构傅里叶伪谱方法的误差估计
DOI：
10.1002/num.22432
复制
发表时间：
2020
影响因子：
3.9
通讯作者：
Wang Pengde
中科院分区：
文献类型：
--
作者：
Fei Mingfa;Huang Chengming;Wang Pengde
This paper gives a rigorous error analysis of the multisymplectic Fourier pseudospectral method for the nonlinear fractional Schrödinger equation. The method preserves some intrinsic structure properties including the generalized multisymplectic conservation law. By rewriting it in a matrix form similar to that in the finite difference method, the method is shown to be convergent in the discreteL2norm with the second‐order accuracy in time and spectral accuracy in space. The key techniques in the analysis include the discrete energy method, cutoff of the nonlinearity, and a posterior bound of numerical solutions by using the inverse inequality. In a similar line, the convergence result for the symplectic Fourier pseudospectral method can also be established. Moreover, the errors in the local and global energy conservation laws of discrete systems are also investigated. Numerical tests are performed to confirm the theoretical results.
