A Meshless Method for the Coupled Nonlinear Schrödinger Equations

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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