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

• Authors: B. Gürbüz , M. Sezer
• Languages of publication: EN

Abstracts

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.

Keywords

EN

02.30.Gp; 02.30.Hq; 02.70

Discipline

• 02.30.Hq: Ordinary differential equations
• 02.30.Gp: Special functions

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2016
• Volume: 130
• Issue: 1
• Pages: 194-197

Dates

published

2016-07

Contributors

author

B. Gürbüz

• Manisa Celal Bayar University, Department of Mathematics, Faculty of Art & Science, Manisa, Turkey

author

M. Sezer

• Manisa Celal Bayar University, Department of Mathematics, Faculty of Art & Science, Manisa, Turkey

References

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Identifiers

DOI

10.12693/APhysPolA.130.194