Work

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

Year: 2024

Type: article

Abstract: In this paper, a linearized Euler Galerkin scheme is studied and the unconditionally optimal error estimate in L 2 -norm is obtained for Schrödinger equation with cubic nonlinearity 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: Applied Mathematics Letters

DOI: 10.1016/j.aml.2024.109401

Author: Huaijun Yang

Institution: Zhengzhou University of Aeronautics

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,690

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