Kürkçü Ö.K.Aslan E.Sezer M.2024-07-222024-07-22201701689274http://akademikarsiv.cbu.edu.tr:4000/handle/123456789/15219In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson polynomial solutions. These solutions are plotted along with the exact solutions in figures and the numerical results are compared with other well-known methods in tables. © 2017 IMACSEnglishConvergence of numerical methodsIntegral equationsNonlinear equationsNumerical methodsProblem solvingCollocation pointsConvergenceConvergence analysisDickson polynomialMatrix methodsNonlinear differential and integral equationsNumerical resultsResidual functionsPolynomialsArticle10.1016/j.apnum.2017.06.015