- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Vol: 71 Issue: 1
- A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a bou...
A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer
Authors : Hayriye Guckir Cakir, Firat Cakir, Musa Çakir
Pages : 51-67
Doi:10.31801/cfsuasmas.946910
View : 7 | Download : 6
Publication Date : 2022-03-30
Article Type : Research
Abstract :We construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equation(SPVIDE) on Bakhvalov-Shishkin mesh. For the discretization of the problem, we use the integral identities and deal with the emerging integrals terms with interpolating quadrature rules which also yields remaining terms. The stability bound and the error estimates of the approximate solution are established. Further, we demonstrate that the scheme on Bakhvalov-Shishkin mesh is N ( O − 1 ) N(O−1) u n iformly convergent, where N is the mesh parameter. The numerical results are also provided for a couple of examples.Keywords : Singularly perturbed, VIDE, , difference schemes, uniform convergence, error estimates