Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations
Abstract
Numerically solving parabolic equations with quasiperiodic coefficients is a significant challenge due to the potential formation of space-filling quasiperiodic structures that lack translational symmetry or decay. In this paper, we introduce a highly accurate numerical method for solving time-dependent quasiperiodic parabolic equations. We discretize the spatial variables using the projection method (PM) and the time variable with the second-order backward differentiation formula (BDF2). We provide a complexity analysis for the resulting PM-BDF2 method. Furthermore, we conduct a detailed convergence analysis, demonstrating that the proposed method exhibits spectral accuracy in space and second-order accuracy in time. Numerical results in both one and two dimensions validate these convergence results, highlighting the PM-BDF2 method as a highly efficient algorithm for addressing quasiperiodic parabolic equations.
Cite
@article{arxiv.2412.19175,
title = {Convergence analysis of PM-BDF2 method for quasiperiodic parabolic equations},
author = {Kai Jiang and Meng Li and Juan Zhang and Lei Zhang},
journal= {arXiv preprint arXiv:2412.19175},
year = {2024}
}