The Legendre Matrix-Collocation Approach for Some Nonlinear Differential Equations Arising in Physics and Mechanics

Year 2019, Issue: 15, 289 - 296, 31.03.2019

Duygu Dönmez Demir Tuğçe Çınardalı Ömür Kıvanç Kürkçü Mehmet Sezer

https://doi.org/10.31590/ejosat.507708

Cited By: 3

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.

Keywords

Legendre polynomials and series, nonlinear ordinary differential equation, matrix method, residual error

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