Introduction

Kuppalapalle Vajravelu () and Robert A. van Gorder ()
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Kuppalapalle Vajravelu: University of Central Florida, Department of Mathematics
Robert A. van Gorder: University of Central Florida, Department of Mathematics

Chapter Chapter 1 in Nonlinear Flow Phenomena and Homotopy Analysis, 2012, pp 1-5 from Springer

Abstract: Abstract The processes in the world we live in are, more often than not, governed by nonlinearity. Hence, in mathematics, and also in many other sciences in which quantitative models are useful, we often wish to obtain solutions for nonlinear equations. In the field of differential equations, many results pertaining to linear differential equations are well known and have been in existence for quite a while. However, in the area of nonlinear differential equations, there is little in the way of a unifying theory. In many cases, exact solutions for nonlinear differential equations are not to be found, and often we must resort to numerical schemes in order to gain an understanding of a solution to a particular nonlinear equation. When exact or analytical solutions are obtained, one often faces with difficulty of generalizing such results to other nonlinear differential equations.

Keywords: Nonlinear Differential Equation; Auxiliary Function; Homotopy Analysis Method; Fractional Partial Differential Equation; Auxiliary Linear Operator (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-32102-3_1

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DOI: 10.1007/978-3-642-32102-3_1

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