Yapman, Ömer; Kudu, Mustafa; Amiraliyev, Gabil M.

In this paper, we study a uniform finite difference method for the first-order singularly perturbed Volterra integro-differential problem depending on a parameter. We prove that the method is uniform second-order convergent except for a logarithmic factor in the discrete maximum norm. Numerical results are presented which are in agreement with the theoretical analysis.

Kudu, Mustafa; Amirali, Ilhame; Amiraliyev, Gabil M.

In this paper, the homogeneous type fitted difference scheme for solving singularly perturbed problem depending on a parameter with integral boundary condition is proposed. We prove that the method is O(N- 2ln N) uniform convergent on Shishkin meshes. Numerical results are also presented.

Durmaz, Muhammet Enes; Amiraliyev, Gabil M.

In this paper, we deal with a fitted second-order homogeneous (non-hybrid) type difference scheme for solving the singularly perturbed linear second-order Fredholm integro-differential equation. The numerical method represents the exponentially fitted scheme on the Shishkin mesh. Numerical example is presented to demonstrate efficiency of proposed method.

Cimen, Erkan; Amiraliyev, Gabil M.

Difference method on a piecewise uniform mesh of Shishkin type, for a singularly perturbed boundary-value problem for a linear second-order delay differential equation is examined. It is proved that it gives essentially a first-order parameter-uniform convergence in the discrete maximum norm. Furthermore, numerical results are presented in support of the theory.