Solution of a Fourth Order Integro-Differential BVP Designed for the Study of Hinged Beam Vibrations: An Iterative Approach

Abstract

This paper focuses on solving a fourth order integro-differential boundary value problem that is designed for the study of hinged beam vibrations or for the study of static deflection arising in suspension bridges. A number of authors have investigated its numerical solution using iterative methods while maintaining efficiency respectively. The most recently established methodology, which involves Green’s function and its embedment with fixed points schemes as that of Picard’s and Krasnoselki–Mann’s, is the approach used in this study in order to achieve efficient numerical solution. The solved numerical examples and their residual error computations endorse the accuracy and efficacy of the proposed technique.