Work

Stability of the Additive Splitting Methods for the Generalized Nonlinear Schrödinger Equation

Year: 2025

Type: article

Abstract: Splitting methods provide an efficient approach to solving evolutionary wave equations, especially in situations where dispersive and nonlinear effects on wave propagation can be separated, as in the generalized nonlinear Schrödinger equation (GNLSE). However, such methods are explicit and can lead to numerical instabilities. We study these instabilities in the context of the GNLSE. Results previously obtained for multiplicative splitting methods are extended to additive splittings. An estimate of the largest possible integration step is derived and tested. The results are important when many solutions of GNLSE are needed, e.g., in optimization problems or statistical calculations.

Source: Mathematics

DOI: 10.3390/math13081301

Authors: Shalva Amiranashvili, Uwe Bandelow, Raimondas Čiegis

Institutions: Weierstrass Institute for Applied Analysis and Stochastics, Vilnius Gediminas Technical University

Language: English

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W4409483287

FWCI: 2.142

Cites: 61

Cited by: 2

Related to: 10