Work

Numerical Simulation of the Time-Fractional Nonlinear Schrödinger Equation and the Time-Fractional Schrödinger–Poisson System

Year: 2026

Type: article

Abstract: This paper presents an efficient localized meshless method for solving the nonlinear time-fractional Schrödinger equation and the time-fractional Schrödinger–Poisson system. The proposed approach consists of two main steps. First, the Caputo time-fractional derivative is approximated using the L1 formula, which has an accuracy of order O(δt2−β) for 0<β<1. The spatial derivatives in the coupled equations are then discretized using a localized radial basis function Hermite finite-difference (LRBF-HFD) method. In this approach, the Laplacian operator is approximated on small overlapping neighborhoods, thereby avoiding the large and ill-conditioned systems arising from global RBF methods. Numerical experiments are presented to confirm the accuracy and reliability of the proposed method.

Source: Mathematics

DOI: 10.3390/math14203731

Authors: Omid Nikan, Zakieh Avazzadeh

Institutions: Iran University of Science and Technology, Stony Brook University

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

OpenAlex ID: W7221787511

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