An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method

In this study, an effective differential quadrature method (DQM) which is based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. After separating the Schrödinger equation into coupled real value differential equations,we have discretized using DQM and then obtained ordinary differential equation systems. For time integration, low storage strong stability-preserving Runge–Kutta method has been used. Numerical solutions of five different test problems have been obtained. The efficiency and accuracy of the method have been measured by calculating error norms L2 and Linfinity and two lowest invariants I1 and I2. Also relative changes of invariants are given. The newly obtained numerical results have been compared with the published numerical results and a comparison has shown that the MCB-DQM is an effective numerical scheme to solve the nonlinear Schrödinger equation. © 2017 Elsevier Ltd

Dergi Adı Chaos, Solitons and Fractals
Dergi Cilt Bilgisi 100
Sayfalar 45 - 56
Yayın Yılı 2017
Eser Adı
[dc.title]
An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method
Yazar
[dc.contributor.author]
Bashan A.
Yazar
[dc.contributor.author]
Yagmurlu N.M.
Yazar
[dc.contributor.author]
Ucar Y.
Yazar
[dc.contributor.author]
Esen A.
Yayın Yılı
[dc.date.issued]
2017
Yayıncı
[dc.publisher]
Elsevier Ltd
Yayın Türü
[dc.type]
article
Özet
[dc.description.abstract]
In this study, an effective differential quadrature method (DQM) which is based on modified cubic B-spline (MCB) has been implemented to obtain the numerical solutions for the nonlinear Schrödinger (NLS) equation. After separating the Schrödinger equation into coupled real value differential equations,we have discretized using DQM and then obtained ordinary differential equation systems. For time integration, low storage strong stability-preserving Runge–Kutta method has been used. Numerical solutions of five different test problems have been obtained. The efficiency and accuracy of the method have been measured by calculating error norms L2 and Linfinity and two lowest invariants I1 and I2. Also relative changes of invariants are given. The newly obtained numerical results have been compared with the published numerical results and a comparison has shown that the MCB-DQM is an effective numerical scheme to solve the nonlinear Schrödinger equation. © 2017 Elsevier Ltd
Kayıt Giriş Tarihi
[dc.date.accessioned]
2019-12-23
Açık Erişim Tarihi
[dc.date.available]
2019-12-23
Yayın Dili
[dc.language.iso]
eng
Konu Başlıkları
[dc.subject]
Differential quadrature method
Konu Başlıkları
[dc.subject]
Modified Cubic B-splines
Konu Başlıkları
[dc.subject]
Partial differential equations
Konu Başlıkları
[dc.subject]
Schrödinger equation
Konu Başlıkları
[dc.subject]
Strong stability-preserving Runge–Kutta
Haklar
[dc.rights]
info:eu-repo/semantics/closedAccess
ISSN
[dc.identifier.issn]
0960-0779
İlk Sayfa Sayısı
[dc.identifier.startpage]
45
Son Sayfa Sayısı
[dc.identifier.endpage]
56
Dergi Adı
[dc.relation.journal]
Chaos, Solitons and Fractals
Dergi Cilt Bilgisi
[dc.identifier.volume]
100
Tek Biçim Adres
[dc.identifier.uri]
https://dx.doi.org/10.1016/j.chaos.2017.04.038
Tek Biçim Adres
[dc.identifier.uri]
https://hdl.handle.net/20.500.12628/4195
Görüntülenme Sayısı ( Şehir )
Görüntülenme Sayısı ( Ülke )
Görüntülenme Sayısı ( Zaman Dağılımı )
Görüntülenme
23
09.12.2022 tarihinden bu yana
İndirme
1
09.12.2022 tarihinden bu yana
Son Erişim Tarihi
08 Nisan 2024 08:27
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Tıklayınız
equation numerical Schrödinger obtained method differential invariants effective nonlinear solutions results efficiency accuracy problems Linfinity calculating lowest measured comparison Elsevier scheme MCB-DQM published compared changes relative different B-spline separating obtain implemented coupled modified quadrature Numerical
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