Series and Integral Representations of Particular Solutions of the Inhomogeneous Airy's Equations

Abstract

M.S. Abu Zaytoon, R.A. Ford and M. H. Hamdan

In this work an overview of the inhomogeneous, classic Airy’s equation and the inhomogeneous generalized Airy’s equation is provided. When the forcing terms are constant, these equations are directly applicable to modelling variations in permeability and the study of flow through porous media with a transition layer. Particular solutions to these equations are expressed in terms of the Nield-Kuznetsov functions of the first find. When the forcing terms are non-constant continuous functions, partic- ular solutions are expressed in terms of the Nield-Kuznetsov functions of the second kind. An investigation of these functions and some of their properties, representations, and higher derivatives, is carried out in this work. Resulting series and integrals when the forcing functions are the Einstein energy functions are presented to illustrate and identify their computational needs.

PDF