Optimal error estimate of a conformal Fourier pseudo‐spectral method for the damped nonlinear Schrödinger equation. Issue 4 (16th April 2018)

• Record Type: Journal Article
• Authors: Jiang, Chaolong; Cai, Wenjun; Wang, Yushun
• Is Part Of: Numerical methods for partial differential equations. Volume 34:Issue 4(2018)
• Page Start: 1422
• Page End: 1454
• Publication Date: 2018-04-16
• Subjects: conformal conservation law -- damped nonlinear schrödinger equation -- fourier pseudo‐spectral method -- priori estimate; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22264
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : In this article, a Fourier pseudospectral method, which preserves the conforal conservation la, is proposed for solving the damped nonlinear Schrödinger equation. Based on the energy method and the semi‐norm equivalence between the Fourier pseudospectral method and the finite difference method, a priori estimate for the new method is established, which shows that the proposed method is unconditionally convergent with order of O ( τ 2 + J 1 − r ) in the discrete L ∞ ‐norm, where τ is the time step and J is the number of collocation points used in the spectral method. Some numerical results are addressed to confirm our theoretical analysis.