THERMAL SCIENCE

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Kübra Erdem Biçer

,

Mehmet Sezer

A COMPUTATIONAL METHOD FOR SOLVING DIFFERENTIAL EQUATIONS WITH QUADRATIC NONLINEARITY BY USING BERNOULLI POLYNOMIALS

ABSTRACT
In this paper, a matrix method is developed to solve quadratic nonlinear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. And both the approximate solution and the main problem are written in matrix form to obtain the solution. The absolute errors are applied to numeric examples to demonstrate efficiency and accuracy of this technique. The obtained tables and figures in the numeric examples show that this method is very sufficient and reliable for solution of nonlinear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds.
KEYWORDS
Bernoulli polynomials, approximate solutions, numerical methods, Nonlinear Differential Equations
PAPER SUBMITTED: 2018-11-28
PAPER REVISED: 2018-12-26
PAPER ACCEPTED: 2019-01-15
PUBLISHED ONLINE: 2019-03-09
DOI REFERENCE: https://doi.org/10.2298/TSCI181128041B
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 1, PAGES [S275 - S283]
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A computational method for solving differential equations with quadratic nonlinearity by using Bernoulli polynomials

© 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