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http://dx.doi.org/10.4134/CKMS.c210261

A ROBUST NUMERICAL TECHNIQUE FOR SOLVING NON-LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS WITH BOUNDARY LAYER  

Cakir, Firat (Department of Mathematics Batman University)
Cakir, Musa (Department of Mathematics Van Yuzuncu Yil University)
Cakir, Hayriye Guckir (Department of Mathematics Adiyaman University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.3, 2022 , pp. 939-955 More about this Journal
Abstract
In this paper, we study a first-order non-linear singularly perturbed 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 exponential 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 results on a couple of examples are also provided to confirm the theoretical analysis.
Keywords
Singularly perturbed; VIDE; difference schemes; uniform convergence; error estimates; Bakhvalov-Shishkin mesh;
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