A novel second-order fitted computational method for a singularly perturbed Volterra integro-differential equation

A second order numerical method for singularly perturbed Volterra integro-differential equations with delay

“…The construction of the difference scheme is a combination of hybrid difference scheme on a Shishkin-type mesh and appropriate quadrature rules. Error estimates are obtained by using the truncation error estimate techniques and a discrete analogue of Grönwall's inequality and it is shown that the scheme is O(N −2 ln 2 N) order convergent, which improves the numerical results given in [7,[12][13][14]. Numerical experiments are presented to support the theoretical result.…”

“…Yapman et al [13] developed a numerical method of integral identities with the use of exponential basis functions and interpolating quadrature rules for a singularly perturbed nonlinear Volterra integro-differential equation with delay and proved that the scheme is first-order uniform convergent. Yapman and Amiraliyev [14] also design a fitted difference operator on a piecewise-uniform mesh by using the exponential basis functions and interpolating quadrature rules to solve a singularly perturbed Volterra integro-differential equation and showed the convergence order of the scheme is O(N −2 ln N).…”

Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers

“…By using the technique of the exact difference approximations [3,4,11,24,25] (see also [22], pp. 207-214), it follows that…”

A new difference method for the singularly perturbed Volterra-Fredholm integro-differential equations on a Shishkin mesh

“…Boundary value problems of SPFIDEs have been investigated in [9]. Authors in [40] have presented second-order discretization on a piecewise uniform mesh for SPVIDEs. The finite difference scheme with exponential coefficient has been established on a uniform mesh for SPFIDEs in [3].…”