A posteriori error bounds for the approximate solution of second-order ODEs by piecewise coefficients perturbation methods

This paper presents a constructive approach to compute upper and lower bounds for the error committed when some second-order ordinary differential equations are solved by means of piecewise coefficients perturbation methods (PPM). The obtained error bounds are expressed in terms of perturbations introduced in the differential operator and in the prescribed initial conditions. The results are applied to collocation, tau and finite difference methods. Numerical examples demonstrating the sharpness of the constructed bounds are given.