An Algebra of Exponential Polynomials as the Cofinite Dual of the Hopf Algebra of Polynomials

We prove that the cofinite dual of the Hopf algebra of polynomials in several variables can be represented as a Hopf algebra ? of exponential polynomials that contains the polynomials as a Hopf subalgebra. We also present some algebras isomorphic to ? whose elements are rational functions or multi-sequences.     

Operational Solution to the Nonlinear Klein-Gordon Equation

We obtain solutions of the nonlinear Klein-Gordon equation using a novel operational method combined with the Adomian polynomial expansion of nonlinear functions. Our operational method does not use any integral transforms nor integration processes. We illustrate the application of our method by solving several examples and present numerical results that show the accuracy of the truncated series approximations to the solutions.     

An operational approach to the Emden–Fowler equation

In this paper, we present a method for solving the Emden–Fowler equation using the Adomian polynomials and the operational calculus introduced by the authors. Copyright © 2015 John Wiley & Sons, Ltd.