Taştekin D.Yalçinbaş S.Sezer M.2024-07-222024-07-2220131300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/17455In this study, we present a reliable numerical approximation of the some first order nonlinear ordinary differential equations with the mixed condition by the using a new Taylor collocation method. The solution is obtained in the form of a truncated Taylor series with easily determined components. Also, the method can be used to solve Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparing the methodology with some known techniques shows that the existing approximation is relatively easy and highly accurate.EnglishAll Open Access; Gold Open AccessNumerical methodsOrdinary differential equationsRiccati equationsCollocation methodCollocation pointsFirst order nonlinear differential equationsHighly accurateNonlinear ordinary differential equationNumerical approximationsNumerical resultsTaylor polynomialsNonlinear equationsArticle10.3390/mca18030383