Pell-Lucas collocation method to solve high-order linear Fredholm-Volterra integro-differential equations and residual correction

Abstract

In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higherorder linear Fredholm-Volterra integro differential equations (FVIDE). The approximate solutions are assumed in formof the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, thesolution form and its derivatives are brought to matrix forms. By applying the collocation method based on equallyspaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of thissystem determines the coefficients of assumed solution. Error estimation is made and also a method with the help of theobtained approximate solution is developed that finds approximate solution with better results. Then, the applicationsare made on five examples to show that the method is successful. In addition, the results are supported by tables andgraphs and the comparisons are made with other methods available in the literature. All calculations in this study havebeen made using codes written in Matlab.