Pell-Lucas collocation method to solve high-order linear Fredholm-Volterra integro-differential equations and residual correction
TURKISH JOURNAL OF MATHEMATICS, vol.44, no.4, pp.1065-1091, 2020 (SCI-Expanded, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 44 Issue: 4
- Publication Date: 2020
- Doi Number: 10.3906/mat-2002-55
- Journal Name: TURKISH JOURNAL OF MATHEMATICS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
- Page Numbers: pp.1065-1091
- Keywords: Collocation method, collocation points, Fredholm-Volterra integro-differential equations, Pell-Lucas poly, nomials, HOMOTOPY PERTURBATION METHOD, NUMERICAL-SOLUTION, BERNSTEIN POLYNOMIALS, INTEGRAL-EQUATIONS, APPROXIMATION METHOD, OPERATIONAL MATRIX, SYSTEM, CONVERGENCE, FORM
- Open Archive Collection: AVESIS Open Access Collection
- Akdeniz University Affiliated: Yes
Abstract
In this article, a collocation method based on Pell-Lucas polynomials is studied to numerically solve higher order linear Fredholm-Volterra integro differential equations (FVIDE). The approximate solutions are assumed in form of the truncated Pell-Lucas polynomial series. By using Pell-Lucas polynomials and relations of their derivatives, the solution form and its derivatives are brought to matrix forms. By applying the collocation method based on equally spaced collocation points, the method reduces the problem to a system of linear algebraic equations. Solution of this system determines the coefficients of assumed solution. Error estimation is made and also a method with the help of the obtained approximate solution is developed that finds approximate solution with better results. Then, the applications are made on five examples to show that the method is successful. In addition, the results are supported by tables and graphs and the comparisons are made with other methods available in the literature. All calculations in this study have been made using codes written in Matlab.