TY - JOUR T1 - Lineer Olmayan İkili Schrödinger Denklemi için Ağsız Bir Yöntem TT - A Meshless Method for the Coupled Nonlinear Schrödinger Equations AU - Karaman, Bahar AU - Dereli, Yılmaz PY - 2019 DA - November DO - 10.29233/sdufeffd.592437 JF - Süleyman Demirel University Faculty of Arts and Science Journal of Science PB - Süleyman Demirel University WT - DergiPark SN - 1306-7575 SP - 418 EP - 435 VL - 14 IS - 2 LA - tr AB - Bu çalışma ağsız biryöntem olan radyal tabanlı fonksiyonlarla kollokasyon (RBFC) yöntemi ile lineerolmayan ikili Schrödinger denklemlerinin (CNLS) sayısal çözümlerinin eldeedilmesi üzerinedir. Zaman ayrıştırması için ileri fark ve kalan terimleriçinde fonksiyonun ardışık zaman adımındaki ortalama değerleri kullanılmıştır.CNLS denklemi için kullanılan yöntemin kararlılık analizi incelemesiVon-Neumann kararlılık metodu kullanılarak yapılmıştır. Metodun geçerliliğinigöstermek için tek soliton dalga hareketi ve iki solitonun etkileşimini içerendört farklı test problemi ele alınmıştır. Her bir test problemi için sayısalsonuçlar grafikler ve tablolar yardımıyla gösterilmiştir. Ayrıca önerilenyöntemin geçerliliğini, verimliliğini ve etkinliğini göstermek için elde edilensayısal sonuçlar analitik ve literatürde var olan sonuçlar ilekarşılaştırılmıştır. KW - RBFC Metodu KW - Von-Neumann Kararlılık Analizi KW - Lineer Olmayan ikili Schrödinger Denklemi N2 - Thecurrent investigation studies a meshfree method based on radial basis functionscollocation method (RBFC) to obtain numerically solutions of the couplednonlinear Schrödinger (CNLS) equations. Forward difference is used for thetemporal discretization and the average value of the function in consecutivetime step is used for other terms. The stability analysis of the proposedmethod is investigated by using Von-Neumann stability technique for thegoverning equations. 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