A Meshless Method for the Coupled Nonlinear Schrödinger Equations

Year 2019, , 418 - 435, 30.11.2019

Bahar Karaman , Yılmaz Dereli

https://doi.org/10.29233/sdufeffd.592437

Cited By: 1

Abstract

The
current investigation studies a meshfree method based on radial basis functions
collocation method (RBFC) to obtain numerically solutions of the coupled
nonlinear Schrödinger (CNLS) equations. Forward difference is used for the
temporal discretization and the average value of the function in consecutive
time step is used for other terms. The stability analysis of the proposed
method is investigated by using Von-Neumann stability technique for the
governing equations. To accuracy of the proposed method, test problems which
include the single soliton motion and two interaction are used. For every test problems,
all obtained numerical results are presented in tables and figures. The
obtained numerical experiments are compared with analytical and published
numerical solutions to confirm the accuracy and efficiency of the suggested
scheme.

Keywords

RBFC method, Coupled nonlinear Schrödinger equations, Von-Neumann stability analysis

Lineer Olmayan İkili Schrödinger Denklemi için Ağsız Bir Yöntem

Abstract

Bu çalışma ağsız bir
yöntem olan radyal tabanlı fonksiyonlarla kollokasyon (RBFC) yöntemi ile lineer
olmayan ikili Schrödinger denklemlerinin (CNLS) sayısal çözümlerinin elde
edilmesi üzerinedir. Zaman ayrıştırması için ileri fark ve kalan terimler
içinde fonksiyonun ardışık zaman adımındaki ortalama değerleri kullanılmıştır.
CNLS denklemi için kullanılan yöntemin kararlılık analizi incelemesi
Von-Neumann kararlılık metodu kullanılarak yapılmıştır. Metodun geçerliliğini
göstermek için tek soliton dalga hareketi ve iki solitonun etkileşimini içeren
dört farklı test problemi ele alınmıştır. Her bir test problemi için sayısal
sonuçlar grafikler ve tablolar yardımıyla gösterilmiştir. Ayrıca önerilen
yöntemin geçerliliğini, verimliliğini ve etkinliğini göstermek için elde edilen
sayısal sonuçlar analitik ve literatürde var olan sonuçlar ile
karşılaştırılmıştır.

Keywords

RBFC Metodu, Von-Neumann Kararlılık Analizi, Lineer Olmayan ikili Schrödinger Denklemi

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