Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method

Mehmet TARAKÇI; Mustafa ÖZEL; Mehmet SEZER

doi:https://doi.org/10.3906/mat-1908-102

Makale detayları

Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method

Yazarlar:

Mehmet TARAKÇI | Mustafa ÖZEL | Mehmet SEZER

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2020 Vol.44 Issue 3, pp.906-918

Belge Tipi:

Makale

Yayın Tarihi:

4/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000745435

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1908-102

Özet:

 

Nonlinear differential equations have many applications in different science and engineering disciplines. However, a nonlinear differential equation cannot be solved analytically and so must be solved numerically. Thus, we aim to develop a novel numerical algorithm based on Morgan-Voyce polynomials with collocation points and operational matrix method to solve nonlinear differential equations. In the our proposed method, the nonlinear differential equations including quadratic and cubic terms having the initial conditions are converted to a matrix equation. In order to obtain the matrix equations and solutions for the selected problems, code was developed in MATLAB. The solution of this method for the convergence and efficiency was compared with the equations such as Van der Pol differential equation calculated by different methods.

Makale detayları

Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method

Yazarlar: Mehmet TARAKÇI | Mustafa ÖZEL | Mehmet SEZER

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2020 Vol.44 Issue 3, pp.906-918

Belge Tipi: Makale

Yayın Tarihi: 4/2020

Belge Dili: İngilizce

Document ID (Org No.): 2000745435

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

DOI: https://doi.org/10.3906/mat-1908-102

Sayı

Yazarlar:

Mehmet TARAKÇI | Mustafa ÖZEL | Mehmet SEZER

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2020 Vol.44 Issue 3, pp.906-918

Belge Tipi:

Makale

Yayın Tarihi:

4/2020

Belge Dili:

İngilizce

Document ID (Org No.):

2000745435

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

DOI:

https://doi.org/10.3906/mat-1908-102