Guler C.Kaya S.O.Sezer M.2024-07-222024-07-22201903549836http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/14763The purpose of this paper is to present a Hermite polynomial approach for solving a high-order ODE with non-linear 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 non-linear 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. © 2019 Society of Thermal Engineers of Serbia.EnglishAll Open Access; Gold Open Access; Green Open AccessLinear equationsMatrix algebraNumerical methodsPolynomialsCollocation methodHermite seriesHermite's polynomialsHigh-order ODEsMatrix methodsNon linearNon-linear ODENonlinear ordinary differential equationNumerical solutionPolynomial approachOrdinary differential equationsArticle10.2298/TSCI181215047G