Browsing by Author "Gurbuz, Bahar"

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    A Reliable Numerical Method for the Singularly Perturbed Nonlinear Differential Equation With an Integral Boundary Condition
    (Ivane Javakhishvili Tbilisi State Univ, 2024) Cakir, Musa; Gurbuz, Bahar; Gunes, Baransel
    This study purposes to present an efficient numerical method for the singularly perturbed nonlinear problems involving an integral boundary condition. Initially, some properties are given for the continuous problem. Then, using interpolating quadrature formulas [3], the finite difference scheme is established on the Bakhvalov-Shishkin mesh (B-S mesh). The error approximations of the suggested scheme are examined in the discrete maximum norm. Finally, some numerical examples are included to confirm the theory.
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    A Second Order Fitted Numerical Method for a Singularly Perturbed Problem With an Integral Boundary Condition
    (Birkhauser, 2025) Gurbuz, Bahar; Çakir, Musa; Güneş, Baransel
    This study provides the new discretization for the singularly perturbed problems with an integral boundary condition. Firstly, some properties of the continuous problem are given. Next, using the interpolating quadrature formulas (Amiraliyev and Mamedov in Turk J Math 19(3):207–222, 1995) and linear basis functions, the second-order difference scheme is generated on Shishkin-type mesh. The convergence and error approximations of the proposed scheme are analyzed. Two numerical examples are included to support the theoretical results. © 2025 Elsevier B.V., All rights reserved.