This paper presents a ε-uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, finite difference is established on non-uniform mesh by using interpolating quadrature rules linear basis functions. An error analysis successfully carried out Boglaev–Bakhvalov-type mesh....

Recent developments have shown that the widely used simplified differential model of Eringen’s nonlocal elasticity in nanobeam analysis is not equivalent to corresponding and initially proposed integral models, pure two-phase model, all cases loading boundary conditions. This has resolved a paradox with solutions are line expected softening effect theory appears other cases. In addition, it rev...