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Dergiler / Avrupa Bilim ve Teknoloji Dergisi / 2019 / Sayı: 15

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
Sayfa
289–296
Yayın Tarihi
2019-03-31
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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.

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri:This solution of this matrix equation yields the Legendre coefficients of the solution function.
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Sonuç & Katkı: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.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Legendre polynomials and series · nonlinear ordinary differential equation · matrix method

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.

Abstract

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.

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Bu Makaleye Atıf Yap

DEMİR, D. D., ÇINARDALI, T., KÜRKÇÜ, Ö. K., SEZER, M. (2019). The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 15, 289–296. https://ajindex.com/articles/471855

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Kaynakça (13)

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