A Galerkin-type approach to solve systems of linear Volterra-Fredholm integro-differential equations

KARAÇAYIR M., YÜZBAŞI Ş.

Turkish Journal of Mathematics, vol.46, no.8, pp.3121-3138, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 8
  • Publication Date: 2022
  • Doi Number: 10.55730/1300-0098.3323
  • 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.3121-3138
  • Keywords: Galerkin method, Method of moments, Method of weighted residuals, Numerical solutions, Systems of linear integro-differential equations, Volterra-fredholm integro-differential equations
  • Akdeniz University Affiliated: Yes

Abstract

© This work is licensed under a Creative Commons Attribution 4.0 International License.The main interest of this paper is to propose a numerical scheme in order to solve linear systems of Volterra-Fredholm integro-differential equations given with mixed conditions. The proposed method is a weighted residual scheme which uses monomials up to a prescribed degree N as the basis functions. By taking inner product of the equation system with the elements of this basis set in a Galerkin-like fashion, the original problem is transformed into a linear algebraic equation system. After a suitable incorporation of the mixed conditions, a final algebraic system is obtained, from which the approximate solutions of the problem are computed. The proposed numerical scheme is illustrated with example problems taken from the literature.