Construction of a global solution for the one dimensional singularly-perturbed boundary value problem

Main Article Content

Samir Karasuljic, Dr
Enes Duvnjakovic, Dr
Vedad Pasic, Dr
http://orcid.org/0000-0003-2115-0422
Elvis Barakovic, Dr
http://orcid.org/0000-0002-3358-1599

Abstract

We consider an approximate solution for the one--dimensional semilinear singularly--perturbed boundary value problem, using the previously obtained numerical values of the boundary value problem in the mesh points and the representation of the exact solution using Green's function. We present an \(\varepsilon\)--uniform convergence of such gained the approximate solutions, in the maximum norm of the order \(\mathcal{O}\left(N^{-1}\right)\) on the observed domain. After that, the constructed approximate solution is repaired and we obtain a solution, which also has \(\varepsilon\)--uniform convergence, but now of order \(\mathcal{O}\left(\ln^2N/N^2\right)\) on \([0,1]\). In the end a numerical experiment is presented to confirm previously shown theoretical results.

Article Details

Section
ART
Author Biographies

Enes Duvnjakovic, Dr, Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Tuzla

Associate Professor

Vedad Pasic, Dr, Department of Mathematics, University of Tuzla

Faculty of Science and Mathematics

Department of Mathematics

Associate Professor

Elvis Barakovic, Dr, Department of Mathematics, Faculty of Natural Sciences and Mathematics, University of Tuzla

Assistant Professor