Numerical analysis for coupled systems of two-dimensional time-space fractional Schrödinger equations with trapping potentials

Yıl 2020, , 1 - 12, 10.01.2020

Betül Hiçdurmaz

https://doi.org/10.25092/baunfbed.673243

Cited By: 1

Öz

In this study general and classical coupled systems of nonlinear time-space fractional Schrödinger equations (TSFSDE) with trapping potentials are investigated with a numerical approach. Theorems on stability of the finite difference schemes for such problems are established and presented with their proofs. Numerical solutions are investigated for one and two-dimensional cases. Convergence rates are proved by numerical experiments. Effect of a trapping potential on such systems is searched throughout the paper.

Anahtar Kelimeler

Coupled system, trapping potential, finite difference method

Tuzaklama potansiyelli iki-boyutlu zaman-yer kesirli türevli Schrödinger denklemlerinin bağlı sistemlerinin sayısal analizi

Öz

Bu çalışmada zaman ve yer boyutlarında kesirli türevli Schrödinger diferansiyel denklemlerinin bağıl sistemlerinin genel ve klasik formları tuzaklama potansiyeli altında sayısal bir yaklaşımla ele alınmıştır. Bu tip problemlerin fark şemalarının kararlılıkları üzerine teoremler kurulmuş ve ispatlarıyla sunulmuştur. Sayısal sonuçlar tek ve iki boyutlu durumlar için incelenmiştir. Yaklaşım mertebeleri sayısal deneylerle ispatlanmıştır. Çalışma boyunca tuzaklama potansiyelinin bu tip sistemler üzerine etkisi araştırılmıştır.

Anahtar Kelimeler

Bağlı sistem, tuzaklama potansiyeli, sonlu farklar metodu

Kaynakça

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