2023/12/27 by Kai Jiang, Jiang, Kai, Shifeng Li +3
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Fractional Differential Equations Solutions #Mathematical functions and polynomials #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2312.16462
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Numerical solving the Schrödinger equation with incommensurate potentials presents a great challenge since its solutions could be space-filling quasiperiodic structures without translational symmetry nor decay. In this paper, we propose two high-accuracy numerical methods to solve the time-dependent quasiperiodic Schrödinger equation. Concretely, we discretize the spatial variables by the quasiperiodic spectral method and the projection method, and the time variable by the second-order operator splitting method. The corresponding convergence analysis is also presented and shows that the proposed methods both have exponential convergence rate in space and second order accuracy in time, respectively. Meanwhile, we analyse the computational complexity of these numerical algorithms. One- and two-dimensional numerical results verify these convergence conclusions, and demonstrate that the projection method is more efficient.