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.
Primary Language  en 

Subjects  Engineering 
Journal Section  Makaleler 
Authors 

Dates 
Publication Date : March 31, 2019 
Bibtex  @conference paper { ejosat507708,
journal = {Avrupa Bilim ve Teknoloji Dergisi},
issn = {},
eissn = {21482683},
address = {},
publisher = {Osman SAĞDIÇ},
year = {2019},
volume = {},
pages = {289  296},
doi = {10.31590/ejosat.507708},
title = {The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics},
key = {cite},
author = {Dönmez Demir, Duygu and Çınardalı, Tuğçe and Kürkçü, Ömür Kıvanç and Sezer, Mehmet}
} 
APA  Dönmez Demir, D , Çınardalı, T , Kürkçü, Ö , Sezer, M . (2019). The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi , (15) , 289296 . DOI: 10.31590/ejosat.507708 
MLA  Dönmez Demir, D , Çınardalı, T , Kürkçü, Ö , Sezer, M . "The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi (2019 ): 289296 <https://dergipark.org.tr/en/pub/ejosat/issue/43603/507708> 
Chicago  Dönmez Demir, D , Çınardalı, T , Kürkçü, Ö , Sezer, M . "The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi (2019 ): 289296 
RIS  TY  JOUR T1  The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics AU  Duygu Dönmez Demir , Tuğçe Çınardalı , Ömür Kıvanç Kürkçü , Mehmet Sezer Y1  2019 PY  2019 N1  doi: 10.31590/ejosat.507708 DO  10.31590/ejosat.507708 T2  Avrupa Bilim ve Teknoloji Dergisi JF  Journal JO  JOR SP  289 EP  296 VL  IS  15 SN  21482683 M3  doi: 10.31590/ejosat.507708 UR  https://doi.org/10.31590/ejosat.507708 Y2  2019 ER  
EndNote  %0 Avrupa Bilim ve Teknoloji Dergisi The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics %A Duygu Dönmez Demir , Tuğçe Çınardalı , Ömür Kıvanç Kürkçü , Mehmet Sezer %T The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics %D 2019 %J Avrupa Bilim ve Teknoloji Dergisi %P 21482683 %V %N 15 %R doi: 10.31590/ejosat.507708 %U 10.31590/ejosat.507708 
ISNAD  Dönmez Demir, Duygu , Çınardalı, Tuğçe , Kürkçü, Ömür Kıvanç , Sezer, Mehmet . "The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi / 15 (March 2019): 289296 . https://doi.org/10.31590/ejosat.507708 
AMA  Dönmez Demir D , Çınardalı T , Kürkçü Ö , Sezer M . The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi. 2019; (15): 289296. 
Vancouver  Dönmez Demir D , Çınardalı T , Kürkçü Ö , Sezer M . The Legendre MatrixCollocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi. 2019; (15): 296289. 