Septic B-spline Collocation Method  for Numerical Solution of the Generalized Nonlinear Schrodinger Equation

Dursun Irk

Article Details

Septic B-spline Collocation Method for Numerical Solution of the Generalized Nonlinear Schrodinger Equation

Authors:

Dursun Irk

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.28-33

Document Type:

Article

Publication Date:

6/2023

Document Language:

Turkish

Document ID (Org No.):

2001287658

pISSN:

2687-606X

Keywords:

Abstract:

 This study introduces to obtain high order accurate method for numerical solution of the generalized nonlinear Schrodinger GNLS equation. Two different time discretizations are used in the study. The first method is the well known Crank-Nicolson method with second order accuracy and the second method discretization is a one-step method with fourth order accuracy. After using a general method including two proposed time discretization methods for time discretization, the collocation method using septic B-spline functions will be used forspace discretization. A non-linear system of equations will be obtained after applying time and space disctretizations. While the equation system is being solved with the help of Matlab package program, firstly an inner iteration linearization will be used and the solutions up to the desired time will be found iteratively. Finally, the proposed methods are tested by using the solitary wave propagation test problem.

 This study introduces to obtain high order accurate method for numerical solution of the generalized nonlinear Schrodinger GNLS equation. Two different time discretizations are used in the study. The first method is the well known Crank-Nicolson method with second order accuracy and the second method discretization is a one-step method with fourth order accuracy. After using a general method including two proposed time discretization methods for time discretization, the collocation method using septic B-spline functions will be used forspace discretization. A non-linear system of equations will be obtained after applying time and space disctretizations. While the equation system is being solved with the help of Matlab package program, firstly an inner iteration linearization will be used and the solutions up to the desired time will be found iteratively. Finally, the proposed methods are tested by using the solitary wave propagation test problem.

 This study introduces to obtain high order accurate method for numerical solution of the generalized nonlinear Schrodinger GNLS equation. Two different time discretizations are used in the study. The first method is the well known Crank-Nicolson method with second order accuracy and the second method discretization is a one-step method with fourth order accuracy. After using a general method including two proposed time discretization methods for time discretization, the collocation method using septic B-spline functions will be used forspace discretization. A non-linear system of equations will be obtained after applying time and space disctretizations. While the equation system is being solved with the help of Matlab package program, firstly an inner iteration linearization will be used and the solutions up to the desired time will be found iteratively. Finally, the proposed methods are tested by using the solitary wave propagation test problem.

 Bu çalışma, genelleştirilmiş lineer olmayan Schordinger GNLS denkleminin yüksek doğruluklu sayısal çözümünü elde etmek içindir. Çalışmada iki farklı zaman parçalanması kullanılacaktır. İlk zaman parçalanması doğruluğu iki olan ve literatürde iyi bilinen Crank-Nicolson yöntemi, ikinci zaman parçalanması ise tek adımlı ve dördüncü mertebeden doğruluğa sahip yöntemdir. Zaman parçalanması için genel bir yöntem kullanıldıktan sonra konum parçalanması için ise septik B-spline fonksiyonların kullanıldığı kolokasyon yöntemi kullanılacaktır. Zaman ve konum parçalanması uygulandıktan sonra lineer olmayan bir denklem sistemi elde edilecektir. Denklem sistemi Matlab paket programı yardımıyla çözülürken öncelikle iç iterasyonlu bir lineerleştirme kullanılacak ve istenilen zaman kadarki çözümler iteratif olarak bulunacaktır Son olarak solitary dalgasının yayılımı test problemi kullanılarak önerilen metotlar test edilmiştir.

Article Details

Septic B-spline Collocation Method for Numerical Solution of the Generalized Nonlinear Schrodinger Equation

Authors:

Dursun Irk

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.28-33

Document Type:

Article

Publication Date:

6/2023

Document Language:

Turkish

Document ID (Org No.):

2001287658

pISSN:

2687-606X

Septic B-splines

Generalized nonlinear Schrodinger equation

Collocation methodSeptik B-spline

Genelleştirilmiş lineer olmayan Schrodinger denklemi

Kolokasyon metodu

Issues

Article Details

Septic B-spline Collocation Method for Numerical Solution of the Generalized Nonlinear Schrodinger Equation

Authors: Dursun Irk

Publisher: Eskişehir Osmangazi University

Main Topics: Bilgisayar Yazılımı

Journal: Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.28-33

Document Type: Article

Publication Date: 6/2023

Document Language: Turkish

Document ID (Org No.): 2001287658

pISSN: 2687-606X

Septic B-splines

Generalized nonlinear Schrodinger equation

Collocation methodSeptik B-spline

Genelleştirilmiş lineer olmayan Schrodinger denklemi

Kolokasyon metodu

Issues

Authors:

Dursun Irk

Publisher:

Eskişehir Osmangazi University

Main Topics:

Bilgisayar Yazılımı

Journal:

Eskişehir Türk Dünyası Uygulama ve Araştırma Merkezi Bilişim Dergisi Vol.4 Issue 2, pp.28-33

Document Type:

Article

Publication Date:

6/2023

Document Language:

Turkish

Document ID (Org No.):

2001287658

pISSN:

2687-606X