A novel approach via mixed Crank–Nicolson scheme and differential quadrature method for numerical solutions of solitons of mKdV equation

The purpose of the present study is to obtain numerical solutions of the modified Korteweg–de Vries equation (mKdV) by using mixed Crank–Nicolson scheme and differential quadrature method based on quintic B-spline basis functions. In order to control the effectiveness and accuracy of the present approximation, five well-known test problems, namely, single soliton, interaction of double solitons, interaction of triple solitons, Maxwellian initial condition and tanh initial condition, are used. Furthermore, the error norms L2 and L? are calculated for single soliton solutions to measure the efficiency and the accuracy of the present method. At the same time, the three lowest conservation quantities are calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants are calculated and presented. After all these processes, the newly obtained numerical results are compared with results of some of the published articles. © 2019, Indian Academy of Sciences.

Dergi Adı Pramana - Journal of Physics
Dergi Cilt Bilgisi 92
Dergi Sayısı 6
Sayfalar -
Yayın Yılı 2019
Eser Adı
[dc.title]
A novel approach via mixed Crank–Nicolson scheme and differential quadrature method for numerical solutions of solitons of mKdV equation
Yazar
[dc.contributor.author]
Başhan A.
Yayın Yılı
[dc.date.issued]
2019
Yayıncı
[dc.publisher]
Springer
Yayın Türü
[dc.type]
article
Özet
[dc.description.abstract]
The purpose of the present study is to obtain numerical solutions of the modified Korteweg–de Vries equation (mKdV) by using mixed Crank–Nicolson scheme and differential quadrature method based on quintic B-spline basis functions. In order to control the effectiveness and accuracy of the present approximation, five well-known test problems, namely, single soliton, interaction of double solitons, interaction of triple solitons, Maxwellian initial condition and tanh initial condition, are used. Furthermore, the error norms L2 and L? are calculated for single soliton solutions to measure the efficiency and the accuracy of the present method. At the same time, the three lowest conservation quantities are calculated and also used to test the efficiency of the method. In addition to these test tools, relative changes of the invariants are calculated and presented. After all these processes, the newly obtained numerical results are compared with results of some of the published articles. © 2019, Indian Academy of Sciences.
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]
02.30.Jr
Konu Başlıkları
[dc.subject]
02.30.Mv
Konu Başlıkları
[dc.subject]
02.60.Cb
Konu Başlıkları
[dc.subject]
02.60.x
Konu Başlıkları
[dc.subject]
differential quadrature method
Konu Başlıkları
[dc.subject]
mKdV equation
Konu Başlıkları
[dc.subject]
Partial differential equations
Konu Başlıkları
[dc.subject]
quintic B-splines
Konu Başlıkları
[dc.subject]
solitons
Haklar
[dc.rights]
info:eu-repo/semantics/closedAccess
ISSN
[dc.identifier.issn]
0304-4289
Dergi Adı
[dc.relation.journal]
Pramana - Journal of Physics
Dergi Sayısı
[dc.identifier.issue]
6
Dergi Cilt Bilgisi
[dc.identifier.volume]
92
Tek Biçim Adres
[dc.identifier.uri]
https://dx.doi.org/10.1007/s12043-019-1751-1
Tek Biçim Adres
[dc.identifier.uri]
https://hdl.handle.net/20.500.12628/3997
Görüntülenme Sayısı ( Şehir )
Görüntülenme Sayısı ( Ülke )
Görüntülenme Sayısı ( Zaman Dağılımı )
Görüntülenme
221
09.12.2022 tarihinden bu yana
İndirme
1
09.12.2022 tarihinden bu yana
Son Erişim Tarihi
11 Haziran 2024 00:59
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Tıklayınız
calculated present method results accuracy single soliton interaction efficiency initial condition numerical solitons solutions quantities conservation lowest measure addition Sciences Academy Indian articles published compared obtained processes presented invariants relative changes triple quadrature differential scheme
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