Duygu DÖNMEZ DEMİR, Tuğçe ÇINARDALI, Ömür Kıvanç KÜRKÇÜ, Mehmet SEZER

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

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.

Anahtar Kelimeler:

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

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

Keywords:

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

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