Work

A high-order method for the numerical approximation of fractional nonlinear Schrödinger equations

Year: 2025

Type: preprint

Abstract: In this paper, the periodic initial-value problem for the fractional nonlinear Schrödinger (fNLS) equation is discretized in space by a Fourier spectral Galerkin method and in time by diagonally implicit, high-order Runge-Kutta schemes, based on the composition with the implicit midpoint rule (IMR). Some properties and error estimates for the semidiscretization in space and for the full discretization are proved. The convergence results and the general performance of the scheme are illustrated with several numerical experiments.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2512.22708

Authors: Durán, A., Reguera, N.

Topic: Numerical methods for differential equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7117690137

Cites:

Cited by:

Related to: