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-
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.