Oʇuz C.Sezer M.2024-07-222024-07-22201500963003http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/16320In this study, a numerical matrix method based on Chelyshkov polynomials is presented to solve the linear functional integro-differential equations with variable coefficients under the initial-boundary conditions. This method transforms the functional equation to a matrix equation by means of collocation points. Also, using the residual function and Mean Value Theorem, an error analysis technique is developed. Some numerical examples are performed to illustrate the accuracy and applicability of the method. © 2015 Elsevier Inc.EnglishBoundary conditionsDifferential equationsIntegrodifferential equationsMatrix algebraAnalysis techniquesChelyshkov polynomials and seriesCollocation methodCollocation pointsFunctional equationResidual errorResidual functionsVariable coefficientsNumerical methodsArticle10.1016/j.amc.2015.03.024