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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. [ABSTRACT FROM AUTHOR]

In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained. [ABSTRACT FROM AUTHOR]

The study deals with an initial-value problem for a singularly perturbed Fredholm integro-differential equation. Parameter explicit theoretical bounds on the continuous solution and its derivative are derived. Parameter uniform error estimates for the approximate solution are established. Numerical results are given to illustrate the parameter-uniform convergence of the numerical approximations. [ABSTRACT FROM AUTHOR]

We study uniform finite-difference method for solving first-order singularly perturbed boundary value problem (BVP) depending on a parameter. Uniform error estimates in the discrete maximum norm are obtained for the numerical solution. Numerical results support the theoretical analysis. [ABSTRACT FROM AUTHOR]

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 - 2 ln N) uniform convergent on Shishkin meshes. Numerical results are also presented. [ABSTRACT FROM AUTHOR]

We consider a uniform finite difference method on a Bakhvalov mesh to solve a quasilinear first order parameterized singularly perturbed problem with integral boundary conditions. Uniform first order error estimates in the discrete maximum norm have been established. Numerical results that demonstrate the sharpness of our theoretical analysis are presented. [ABSTRACT FROM AUTHOR]

We consider a uniform finite difference method on a Bakhvalov mesh to solve a quasilinear first order parameterized singularly perturbed problem with integral boundary conditions. Uniform first order error estimates in the discrete maximum norm have been established. Numerical results that demonstrate the sharpness of our theoretical analysis are presented. [ABSTRACT FROM AUTHOR]