A NUMERICAL SOLUTION STUDY ON SINGULARLY PERTURBED CONVECTION-DIFFUSION NONLOCAL BOUNDARY PROBLEM


Arslan D., Çakır M.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.68, ss.1482-1491, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 68 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.31801/cfsuasmas.540631
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.1482-1491

Özet

This important numerical method is given for the numerical solution of singularly perturbed convection-diffusion nonlocal boundary value problem. First, the behavior of the exact solution is analyzed, which is needed for analysis of the numerical solution in later sections. Next, uniformly convergent finite difference scheme on a Shishkin mesh is established, which is based on the method of integral identities with the use exponential basis functions and interpolating quadrature rules with weight and remainder term in integral form. It is shown that the method is first order accurate expect for a logarithmic factor, in the discrete maximum norm. Finally, the numerical results are presented in table and graphs, and these results reveal the validity of the theoretical results of our method.