Güner A.Yalçinbaş S.2024-07-222024-07-2220131300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/17378In this study, a matrix method based on Legendre collocation points on interval [-1,1] is proposed for the approximate solution of the some first order nonlinear ordinary differential equations with the mixed conditions in terms of Legendre polynomials. The method by means of Legendre collocation points, transforms the differential equation to a matrix equation which corresponds to a system of nonlinear algebraic equations with unknown Legendre coefficients. Also, the method can be used for solving Riccati equation. The numerical results show the effectuality of the method for this type of equations. Comparisons are made between the obtained solution and the exact solution.EnglishAll Open Access; Gold Open AccessMathematical transformationsMatrix algebraNumerical methodsOrdinary differential equationsPolynomialsRiccati equationsApproximate solutionLegendre coefficientLegendre collocationsLegendre polynomialsLegendre-collocation methodNonlinear algebraic equationsNonlinear differential equationNonlinear ordinary differential equationNonlinear equationsLegendre collocation method for solving nonlinear differential equationsArticle10.3390/mca18030521