A numerical method to solve a class of linear integro-differential equations with weakly singular kernel

YÜZBAŞI Ş., Sezer M.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.35, no.6, pp.621-632, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 6
  • Publication Date: 2012
  • Doi Number: 10.1002/mma.1559
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.621-632
  • Keywords: singular Volterra integro-differential equations, integro-differential equations, Abel's integral equations, collocation method, collocation points, Bessel polynomials and series, POLYNOMIAL SOLUTIONS, INTEGRAL-EQUATIONS, FREDHOLM, INVERSION
  • Akdeniz University Affiliated: Yes

Abstract

In this paper, a collocation method based on the Bessel polynomials is introduced for the approximate solution of a class of linear integro-differential equations with weakly singular kernel under the mixed conditions. The exact solution can be obtained if the exact solution is polynomial. In other cases, increasing number of nodes, a good approximation can be obtained with applicable errors. In addition, the method is presented with error and stability analysis. Copyright (c) 2012 John Wiley & Sons, Ltd.