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Dergiler / Turkish Journal of Mathematics / 2020 / Cilt: 44 - Sayı: 3

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

Mehmet TARAKÇI
Mustafa ÖZEL
Mehmet SEZER
Sayfa
906–918
Yayın Tarihi
2020-05-01
DOI
—
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Nonlinear differential equations have many applications in different science and engineering disciplines.
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Temel Bulgular & Veri:However, a nonlinear differential equation cannot be solved analytically and so must be solved numerically.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonlinear ordinary differential equations · Morgan-Voyce polynomials · matrix-collocation method

Abstract

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.

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Bu Makaleye Atıf Yap

TARAKÇI, M., ÖZEL, M., SEZER, M. (2020). Solution of nonlinear ordinary differential equations with quadratic and cubic terms by Morgan-Voyce matrix-collocation method. Turkish Journal of Mathematics, Cilt: 44 - Sayı: 3, 906–918. https://ajindex.com/articles/193193

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Kaynakça (13)

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