A new numerical approach for a singularly perturbed problem with two integral boundary conditions

Çakır M., Arslan D.

COMPUTATIONAL & APPLIED MATHEMATICS, vol.40, no.6, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 6
  • Publication Date: 2021
  • Doi Number: 10.1007/s40314-021-01577-5
  • Journal Name: COMPUTATIONAL & APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Singular perturbation equation, Finite difference scheme, Piecewise uniform mesh, Uniform convergence, Integral conditions, DIFFERENTIAL-EQUATIONS, DIFFUSION TYPE, EXISTENCE, UNIQUENESS, THEOREMS, SCHEME
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this study, finite difference method on a Shishkin mesh is applied to solve the singularly perturbed problem with integral boundary conditions. Some properties of the exact solution are obtained. Finite difference scheme on this mesh is constructed. The stability and convergence analysis of the method are shown as first-order convergent at the discrete maximum norm, regardless of the perturbation parameter e. Numerical results are shown by solving an example on the table and figure.