A computational method for solving differential equations with quadratic non-linearity by using bernoulli polynomials

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dc.contributor.authorBicer K.E.
dc.contributor.authorSezer M.
dc.date.accessioned2024-07-22T08:09:17Z
dc.date.available2024-07-22T08:09:17Z
dc.date.issued2019
dc.description.abstractIn this paper, a matrix method is developed to solve quadratic non-linear differential equations. It is assumed that the approximate solutions of main problem which we handle primarily, is in terms of Bernoulli polynomials. 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 non-linear equations. Also, a formula is utilized based on residual functions and mean value theorem to seek error bounds. © 2019 Society of Thermal Engineers of Serbia.
dc.identifier.DOI-ID10.2298/TSCI181128041B
dc.identifier.issn03549836
dc.identifier.urihttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/14768
dc.language.isoEnglish
dc.publisherSerbian Society of Heat Transfer Engineers
dc.rightsAll Open Access; Gold Open Access
dc.subjectComputation theory
dc.subjectDifferential equations
dc.subjectError analysis
dc.subjectMatrix algebra
dc.subjectPolynomials
dc.subjectAbsolute error
dc.subjectApproximate solution
dc.subjectBernoulli polynomials
dc.subjectFunction values
dc.subjectMatrix forms
dc.subjectMatrix methods
dc.subjectNon-linear equations
dc.subjectNonlinear differential equation
dc.subjectQuadratic nonlinearities
dc.subjectResidual functions
dc.subjectNumerical methods
dc.titleA computational method for solving differential equations with quadratic non-linearity by using bernoulli polynomials
dc.typeArticle

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