Yalçinbas S.Özsoy N.Sezer M.2024-07-222024-07-2220101300686Xhttp://akademikarsiv.cbu.edu.tr:4000/handle/123456789/18486In this paper, a new approximate method for solving higher-order linear ordinary differential equations with variable coefficients under the mixed conditions is presented. The method is based on the rational Chebyshev (RC) Tau, Chebyshev and Taylor collocation methods. The solution is obtained in terms of rational Chebyshev (RC) functions. Also, illustrative examples are given to demonstrate the validity and applicability of the method. © Association for Scientific Research.EnglishAll Open Access; Gold Open AccessRational functionsApproximate methodsApproximate solutionChebyshev collocation methodChebyshev functionsHigher-order ordinary differential equationLinear differential equationLinear ordinary differential equationsVariable coefficientsOrdinary differential equationsArticle10.3390/mca15010045