The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Duygu DÖNMEZ DEMİR; Tuğçe ÇINARDALI; Ömür Kıvanç KÜRKÇÜ; Mehmet SEZER

doi:https://doi.org/10.31590/ejosat.507708

Makale detayları

The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Yazarlar:

Duygu DÖNMEZ DEMİR | Tuğçe ÇINARDALI | Ömür Kıvanç KÜRKÇÜ | Mehmet SEZER

Yayıncı:

Osman SAĞDIÇ

Ana Başlıklar:

Uygulamalı fizik

Dergi:

European Journal of Science and Technology 2019 Vol. Issue 15, pp.289-296

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000920133

Sıklık:

Üç Aylık

eISSN:

2148-2683

DOI:

https://doi.org/10.31590/ejosat.507708

Anahtar kelimeler:

Özet:

 


In this study, the Legendre operational matrix
method based on collocation point is introduced to solve high order ordinary
differential equations with some nonlinear terms arising in physics and
mechanics. This technique transforms the nonlinear differential equation via
mixed conditions into a matrix equation with unknown Legendre coefficients.
This solution of this matrix equation yields the Legendre coefficients of the
solution function. Thus, the approximate solution is obtained in terms of
Legendre polynomials. Some test problems together with residual error
estimation are given to show the usefulness and applicability of the method and
the numerical results are compared.


.

 


In this study, the Legendre operational matrix
method based on collocation point is introduced to solve high order ordinary
differential equations with some nonlinear terms arising in physics and
mechanics. This technique transforms the nonlinear differential equation via
mixed conditions into a matrix equation with unknown Legendre coefficients.
This solution of this matrix equation yields the Legendre coefficients of the
solution function. Thus, the approximate solution is obtained in terms of
Legendre polynomials. Some test problems together with residual error
estimation are given to show the usefulness and applicability of the method and
the numerical results are compared.


.

Makale detayları

The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Yazarlar:

Duygu DÖNMEZ DEMİR | Tuğçe ÇINARDALI | Ömür Kıvanç KÜRKÇÜ | Mehmet SEZER

Yayıncı:

Osman SAĞDIÇ

Ana Başlıklar:

Uygulamalı fizik

Dergi:

European Journal of Science and Technology 2019 Vol. Issue 15, pp.289-296

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000920133

Sıklık:

Üç Aylık

eISSN:

2148-2683

DOI:

https://doi.org/10.31590/ejosat.507708

Legendre polynomials and series

nonlinear ordinary differential equation

matrix method

residual error

Sayı

Makale detayları

The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Yazarlar: Duygu DÖNMEZ DEMİR | Tuğçe ÇINARDALI | Ömür Kıvanç KÜRKÇÜ | Mehmet SEZER

Yayıncı: Osman SAĞDIÇ

Ana Başlıklar: Uygulamalı fizik

Dergi: European Journal of Science and Technology 2019 Vol. Issue 15, pp.289-296

Belge Tipi: Makale

Yayın Tarihi: 3/2019

Belge Dili: İngilizce

Document ID (Org No.): 2000920133

Sıklık: Üç Aylık

eISSN: 2148-2683

DOI: https://doi.org/10.31590/ejosat.507708

Legendre polynomials and series

nonlinear ordinary differential equation

matrix method

residual error

Sayı

Yazarlar:

Duygu DÖNMEZ DEMİR | Tuğçe ÇINARDALI | Ömür Kıvanç KÜRKÇÜ | Mehmet SEZER

Yayıncı:

Osman SAĞDIÇ

Ana Başlıklar:

Uygulamalı fizik

Dergi:

European Journal of Science and Technology 2019 Vol. Issue 15, pp.289-296

Belge Tipi:

Makale

Yayın Tarihi:

3/2019

Belge Dili:

İngilizce

Document ID (Org No.):

2000920133

Sıklık:

Üç Aylık

eISSN:

2148-2683

DOI:

https://doi.org/10.31590/ejosat.507708