Overview
- Offers an introduction to the Optimal Auxiliary Functions Method and applies it to various engineering problems
- Provides a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical system
- Shows applications in fluid mechanics, thermodynamics, nonlinear oscillations electrical machines, and much more
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Table of contents (31 chapters)
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Front Matter
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A Short Introduction to the Optimal Auxiliary Functions Method
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Front Matter
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The Optimal Auxiliary Functions Method in Engineering Applications
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Front Matter
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Keywords
About this book
This book presents the optimal auxiliary functions method and applies it to various engineering problems and in particular in boundary layer problems. The cornerstone of the presented procedure is the concept of “optimal auxiliary functions” which are needed to obtain accurate results in an efficient way. Unlike other known analytic approaches, this procedure provides us with a simple but rigorous way to control and adjust the convergence of the solutions of nonlinear dynamical systems. The optimal auxiliary functions are depending on some convergence-control parameters whose optimal values are rigorously determined from mathematical point of view. The capital strength of our procedure is its fast convergence, since after only one iteration, we obtain very accurate analytical solutions which are very easy to be verified. Moreover, no simplifying hypothesis or assumptions are made.
The book contains a large amount of practical models from various fields of engineering such asclassical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines, and many more.
The book is a continuation of our previous books “Nonlinear Dynamical Systems in Engineering. Some Approximate Approaches”, Springer-2011 and “The Optimal Homotopy Asymptotic Method. Engineering Applications”, Springer-2015.
Authors and Affiliations
Bibliographic Information
Book Title: Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems
Authors: Vasile Marinca, Nicolae Herisanu, Bogdan Marinca
DOI: https://doi.org/10.1007/978-3-030-75653-6
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-75652-9Published: 15 July 2021
Softcover ISBN: 978-3-030-75655-0Published: 16 July 2022
eBook ISBN: 978-3-030-75653-6Published: 14 July 2021
Edition Number: 1
Number of Pages: XIII, 479
Number of Illustrations: 28 b/w illustrations, 414 illustrations in colour
Topics: Materials Science, general, Analysis, Thermodynamics, Engineering Fluid Dynamics, Surfaces and Interfaces, Thin Films