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  1. 3 Acta Physica Polonica A

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  1. 2 2017

  2. 1 2016

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  1. 3 Gürbüz B.

  2. 3 Sezer M.

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Laguerre Polynomial Solutions of a Class of Initial and Boundary Value Problems Arising in Science and Engineering Fields

100%
Gürbüz B., Sezer M.
Acta Physica Polonica A
|
2016
|
vol. 130
|
issue 1
194-197
EN
In this study, we consider high-order nonlinear ordinary differential equations with the initial and boundary conditions. These kinds of differential equations are essential tools for modelling problems in physics, biology, neurology, engineering, ecology, economy, astrophysics, physiology and so forth. Each of the mentioned problems are described by one of the following equations with the specific physical conditions: Riccati, Duffing, Emden-Fowler, Lane Emden type equations. We seek the approximate solution of these special differential equations by means of a operational matrix technique, called the Laguerre collocation method. The proposed method is based on the Laguerre series expansion and the collocation points. By using the method, the mentioned special differential equations together with conditions are transformed into a matrix form which corresponds to a system of nonlinear algebraic equations with unknown Laguerre coefficients, and thereby the problem is approximately solved in terms of Laguerre polynomials. In addition, some numerical examples are presented to demonstrate the efficiency of the proposed method and the obtained results are compared with the existing results in literature.
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Laguerre Polynomial Solutions of a Class of Delay Partial Functional Differential Equations

100%
Gürbüz B., Sezer M.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 3
558-560
EN
In this study, we develop a novel matrix collocation method based on the Laguerre polynomials to find the approximate solutions of some parabolic delay differential equations with integral terms subject to appropriate initial and boundary conditions. The method reduces the solution of the mentioned equations to the solution of a matrix equation which corresponds to system of algebraic equations with unknown Laguerre coefficients. Besides, the error analysis together with numerical results are performed to illustrate the efficiency of our method computationally.
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A New Computational Method Based on Laguerre Polynomials for Solving Certain Nonlinear Partial Integro Differential Equations

100%
Gürbüz B., Sezer M.
Acta Physica Polonica A
|
2017
|
vol. 132
|
issue 3
561-563
EN
In this study, we consider some nonlinear partial integro-differential equations. Most of these equations are used as mathematical models in many problems of physics, biology, chemistry, engineering, and in other areas. Our main purpose is to propose a new numerical method based on the Laguerre and Taylor polynomials, called matrix collocation method, for the numerical solution of the mentioned nonlinear equations under the initial or boundary conditions. To show the effectiveness of this approach, some examples along with error estimations are illustrated by tables and figures.
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