Work

A new error analysis of a linearized BDF2 Galerkin scheme for Schrödinger equation with cubic nonlinearity

Year: 2025

Type: article

Abstract: In this paper, a linearized 2-step backward differentiation formula (BDF2) Galerkin method is proposed and investigated for Schrödinger equation with cubic nonlinearity and unconditionally optimal error estimate in L 2 -norm is obtained without any time-step restriction. The key to the analysis is to bound the H 1 -norm between the numerical solution and the Ritz projection of the exact solution by mathematical induction for two cases rather than the error splitting technique used in the previous work. Finally, some numerical results are presented to confirm the theoretical analysis.

Source: Computers & Mathematics with Applications

DOI: 10.1016/j.camwa.2025.03.025

Author: Huaijun Yang

Institution: Zhengzhou University of Aeronautics

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,170

Funders: National Natural Science Foundation of China, Key Scientific Research Project of Colleges and Universities in Henan Province