TY  - JOUR
T1  - The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics
TT  - The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics
AU  - Dönmez Demir, Duygu
AU  - Çınardalı, Tuğçe
AU  - Kürkçü, Ömür Kıvanç
AU  - Sezer, Mehmet
PY  - 2019
DA  - March
DO  - 10.31590/ejosat.507708
JF  - Avrupa Bilim ve Teknoloji Dergisi
JO  - EJOSAT
PB  - Osman SAĞDIÇ
WT  - DergiPark
SN  - 2148-2683
SP  - 289
EP  - 296
IS  - 15
LA  - en
AB  - In this study, the Legendre operational matrixmethod based on collocation point is introduced to solve high order ordinarydifferential equations with some nonlinear terms arising in physics andmechanics. This technique transforms the nonlinear differential equation viamixed conditions into a matrix equation with unknown Legendre coefficients.This solution of this matrix equation yields the Legendre coefficients of thesolution function. Thus, the approximate solution is obtained in terms ofLegendre polynomials. Some test problems together with residual errorestimation are given to show the usefulness and applicability of the method andthe numerical results are compared.
KW  - Legendre polynomials and series
KW  - nonlinear ordinary differential equation
KW  - matrix method
KW  - residual error
N2  - In this study, the Legendre operational matrixmethod based on collocation point is introduced to solve high order ordinarydifferential equations with some nonlinear terms arising in physics andmechanics. This technique transforms the nonlinear differential equation viamixed conditions into a matrix equation with unknown Legendre coefficients.This solution of this matrix equation yields the Legendre coefficients of thesolution function. Thus, the approximate solution is obtained in terms ofLegendre polynomials. Some test problems together with residual errorestimation are given to show the usefulness and applicability of the method andthe numerical results are compared.
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UR  - https://doi.org/10.31590/ejosat.507708
L1  - https://dergipark.org.tr/tr/download/article-file/663714
ER  -