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## trenThe Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and MechanicsThe Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

#### Duygu Dönmez Demir [1] , Tuğçe Çınardalı [2] , Ömür Kıvanç Kürkçü [3] , Mehmet Sezer [4]

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.

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Primary Language en Engineering Makaleler Orcid: 0000-0003-0886-624XAuthor: Duygu Dönmez Demir (Primary Author)Institution: MANISA CELAL BAYAR UNIVERSITYCountry: Turkey Orcid: 0000-0000-0000-0000Author: Tuğçe ÇınardalıInstitution: İzmir Özel Türk KolejiCountry: Turkey Orcid: 0000-0000-0000-0000Author: Ömür Kıvanç KürkçüInstitution: IZMIR UNIVERSITY OF ECONOMICSCountry: Turkey Orcid: 0000-0000-0000-0000Author: Mehmet SezerInstitution: MANISA CELAL BAYAR UNIVERSITYCountry: Turkey Publication Date : March 31, 2019
 Bibtex @conference paper { ejosat507708, journal = {Avrupa Bilim ve Teknoloji Dergisi}, issn = {}, eissn = {2148-2683}, address = {}, publisher = {Osman SAĞDIÇ}, year = {2019}, volume = {}, pages = {289 - 296}, doi = {10.31590/ejosat.507708}, title = {The Legendre Matrix-Collocation 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 Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi , (15) , 289-296 . DOI: 10.31590/ejosat.507708 MLA Dönmez Demir, D , Çınardalı, T , Kürkçü, Ö , Sezer, M . "The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi (2019 ): 289-296 Chicago Dönmez Demir, D , Çınardalı, T , Kürkçü, Ö , Sezer, M . "The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi (2019 ): 289-296 RIS TY - JOUR T1 - The Legendre Matrix-Collocation 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 - -2148-2683 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 Matrix-Collocation 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 Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics %D 2019 %J Avrupa Bilim ve Teknoloji Dergisi %P -2148-2683 %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 Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics". Avrupa Bilim ve Teknoloji Dergisi / 15 (March 2019): 289-296 . https://doi.org/10.31590/ejosat.507708 AMA Dönmez Demir D , Çınardalı T , Kürkçü Ö , Sezer M . The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi. 2019; (15): 289-296. Vancouver Dönmez Demir D , Çınardalı T , Kürkçü Ö , Sezer M . The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics. Avrupa Bilim ve Teknoloji Dergisi. 2019; (15): 296-289.