A numerical method on Bakhvalov-Shishkin mesh for Volterra integro-differential equations with a boundary layer

Authors : Hayriye GUCKİR CAKİR, Firat CAKİR, Musa ÇAKIR

Pages : 51-67

Doi:10.31801/cfsuasmas.946910

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Publication Date : 2022-03-30

Article Type : Research Paper

Abstract :We construct a finite difference scheme for a first-order linear singularly perturbed Volterra integro-differential equationinsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values( O − 1 ); Ninsert ignore into journalissuearticles values(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