A Robust Numerical Technique for Solving Non-linear Volterra Integro-Differential Equations with Boundary Layer
Commun. Korean Math. Soc.
Published online May 13, 2022
Firat Cakir, Musa Cakir, and Hayriye Guckir Cakir
Batman University; Van Yuzuncu Yil University; Adiyaman University
Abstract : In this paper, we study a first-order non-linear singularly perturbed Volterra integro-
diff erential equation(SPVIDE). We discretize the problem by a uniform diff erence 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 eff ective 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 confi rm the theoretical analysis.
Keywords : Singularly perturbed; VIDE; Di fference schemes; Uniform convergence; Error estimates, Bakhvalov-Shishkin mesh.
MSC numbers : 65L11; 65L12; 65L20; 65R20; 45G05
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