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

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YÜZBAŞI Ş., YILDIRIM G.

TURKISH JOURNAL OF MATHEMATICS, cilt.44, sa.4, ss.1065-1091, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3906/mat-2002-55
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.1065-1091
  • Anahtar Kelimeler: 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
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.