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Introduction

  • Chapter
Nonlinear Flow Phenomena and Homotopy Analysis

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, Florida, 32816 - 1364, USA

    Kuppalapalle Vajravelu & Robert A. van Gorder

Authors
  1. Kuppalapalle Vajravelu
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  2. Robert A. van Gorder
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© 2012 Higher Education Press, Beijing and Springer-Verlag Berlin Heidelberg

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Vajravelu, K., van Gorder, R.A. (2012). Introduction. In: Nonlinear Flow Phenomena and Homotopy Analysis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32102-3_1

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