Bicer K.E.Sezer M.2024-07-222024-07-22201903549836http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/14768In 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.EnglishAll Open Access; Gold Open AccessComputation theoryDifferential equationsError analysisMatrix algebraPolynomialsAbsolute errorApproximate solutionBernoulli polynomialsFunction valuesMatrix formsMatrix methodsNon-linear equationsNonlinear differential equationQuadratic nonlinearitiesResidual functionsNumerical methodsArticle10.2298/TSCI181128041B