A Galerkin-like approach to solve high-order integro-differential equations with weakly singular kernel

YÜZBAŞI Ş., KARAÇAYIR M.

KUWAIT JOURNAL OF SCIENCE, vol.43, no.2, pp.106-120, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 2
  • Publication Date: 2016
  • Journal Name: KUWAIT JOURNAL OF SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.106-120
  • Keywords: Galerkin method, inner product, integro-differential equations, residual error correction, weakly singular kernel, HOMOTOPY PERTURBATION METHOD, INTEGRAL-EQUATIONS, POLYNOMIAL SOLUTIONS, NUMERICAL-SOLUTIONS
  • Akdeniz University Affiliated: Yes

Abstract

In this study, a Galerkin-like approach is applied to numerically solve high-order integro-differential equations having weakly singular kernel. The method includes taking inner product of a set of monomials with a vector obtained from the equation in question. The resulting linear system is then solved, yielding a polynomial as the approximate solution. Additionally, the technique of residual correction, which aims to increase the accuracy of the approximate solution, is discussed briefly. Lastly, the method and the residual correction technique are illustrated with several examples. The results are also compared with numerous existing methods from the literature.