THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Coskun Guler

,

Saba Ozge Kaya

,

Mehmet Sezer

NUMERICAL SOLUTIONS OF A CLASS OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS IN HERMITE SERIES

ABSTRACT
The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ordinary differential equation with nonlinear terms under mixed conditions. The method we used is a matrix method based on collocation points together with truncated Hermite series and reduces the solution of equation to solution of a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Hermite coefficients. In addition, to illustrate the validity and applicability of the method, some numerical examples together with residual error analysis are performed and the obtained results are compared with the existing result in literature.
KEYWORDS
Hermite polynomials and series, nonlinear ordinary differential equations, matrix and collocation method
PAPER SUBMITTED: 2018-12-15
PAPER REVISED: 2018-12-30
PAPER ACCEPTED: 2019-01-10
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI181215047G
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S339 - S351]
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Numerical solutions of a class of nonlinear ordinary differential equations in Hermite series

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence