Cakir, FiratCakir, MusaCakir, Hayriye Guckir2025-05-102025-05-1020221225-17632234-302410.4134/CKMS.c2102612-s2.0-85135529154https://doi.org/10.4134/CKMS.c210261https://hdl.handle.net/20.500.14720/8303In this paper, we study a first-order non-linear singularly per-turbed Volterra integro-differential equation (SPVIDE). We discretize the problem by a uniform difference scheme on a Bakhvalov-Shishkin mesh. The scheme is constructed by the method of integral identities with expo-nential basis functions and integral terms are handled with interpolating quadrature rules with remainder terms. An effective quasi-linearization technique is employed for the algorithm. We establish the error estimates and demonstrate that the scheme on Bakhvalov-Shishkin mesh is O(N-1) uniformly convergent, where N is the mesh parameter. The numerical re-sults on a couple of examples are also provided to confirm the theoretical analysis.eninfo:eu-repo/semantics/closedAccessSingularly PerturbedVideDifference SchemesUniform Con-VergenceError EstimatesBakhvalov-Shishkin MeshArticle373N/AQ4939955WOS:000880304500023