Pell–Lucas polynomial method for Volterra integral equations of the second kind

Lukonde A. P., Demir D. D., Emadifar H., Khademi M., Azizi H.

Afrika Matematika, vol.34, no.3, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 34 Issue: 3
  • Publication Date: 2023
  • Doi Number: 10.1007/s13370-023-01096-y
  • Journal Name: Afrika Matematika
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Keywords: Pell–Lucas polynomials and series, Residual error analysis and absolute error, Volterra Integral equations
  • Karadeniz Technical University Affiliated: Yes

Abstract

This paper introduces a Pell-Lucas collocation method for solving Volterra integral equations of the second kind. The proposed method employs collocation points and represents Pell–Lucas polynomials and their derivatives in matrix vector form. By utilizing this approach, Volterra integral equations are converted into a matrix equation, wherein the undetermined coefficients correspond to the Pell–Lucas coefficients. The effectiveness and efficiency of the proposed method are demonstrated through numerical examples, which yield accurate solutions. The accuracy of these solutions is further assessed using absolute and residual error analysis. Moreover, the obtained numerical results obtained via the Pell–Lucas collocation method are compared with analytical solutions in tables and figures, thus providing a comprehensive evaluation of the method's performance.