A numerical approach for solving nonlinear Fredholm integro-differential equation with boundary layer

Çakır M., Ekinci Y., Çimen E.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.41, no.6, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1007/s40314-022-01933-z
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Singular perturbation, Initial-value problem, Fredholm integro-differential equation, Uniform convergence, Shishkin mesh, COLLOCATION METHOD
  • Van Yüzüncü Yıl University Affiliated: Yes


The study deals with an initial-value problem for a singularly perturbed nonlinear Fredholm integro-differential equation. Parameter explicit theoretical bounds on the continuous solution and its derivative are derived. To solve the approximate solution to this problem, a new difference scheme is constructed with the finite difference method by using the interpolated quadrature rules with the remaining terms in integral form. Parameter uniform error estimates for the approximate solution are established. It is proved that the method converges in the discrete maximum norm, uniformly with respect to the perturbation parameter. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations.