Author:
Gunes Baransel,Cakir Musa
Abstract
UDC 517.9
We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra–Fredholm integro-differential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain the approximate solution of the presented problem. It is proven that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Reference52 articles.
1. N. Adzic, Spectral approximation and nonlocal boundary value problems, Novi Sad J. Math., 30, 1–10 (2000).
2. G. M. Amiraliyev, Ya. D. Mamedov, Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations, Turk. J. Math., 19, № 3, 207–222 (1995).
3. G. M. Amiraliyev, H. Duru, A note on a parameterized singular perturbation problem, J. Comput. and Appl. Math., 182, № 1, 233–242 (2005).
4. D. Arslan, M. Cakir, A numerical solution study on singularly perturbed convection-diffusion nonlocal boundary problem, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. and Stat., 68, № 2, 1482–1491 (2019).
5. D. Arslan, M. Cakir, Y. Masiha, A novel numerical approach for solving convection-diffusion problem with boundary layer behavior, Gazi Univ. J. Sci., 33, № 1, 152–162 (2020).