Demir, Duygu DönmezLukonde, Alpha PeterKürkçü, Ömür KıvançSezer, Mehmet2021-12-132021-12-1320212008-13592251-7456https://doi.org/10.1007/s40096-020-00370-5https://hdl.handle.net/20.500.13091/484In this study, a Pell-Lucas matrix-collocation method is used to solve a class of Fredholm-type delay integro-differential equations with variable delays under initial conditions. The method involves the basic matrix structures gained from the expansions of the functions at collocation points. Therefore, it performs direct and immediate computation. To test its advantage on the applications, some numerical examples are evaluated. These examples show that the method enables highly accurate solutions and approximations. Besides, the accuracy of the solutions and the validity of the method are checked via the residual error analysis and the upper bound error, respectively. Finally, the numerical results, such as errors and computation time, are compared in the tables and figures.eninfo:eu-repo/semantics/closedAccessPell–Lucas polynomials and seriesFredholm-type delay integro-differential equationsMatrix-collocation methodVariable delaysPOLYNOMIAL SOLUTIONSArticle10.1007/s40096-020-00370-52-s2.0-85119506063