Vasile Marinca's Books

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

By: Vasile Marinca,Nicolae Herisanu,Bogdan Marinca

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Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

By: Vasile Marinca,Nicolae Herisanu,Bogdan Marinca

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 as classical 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.

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479

Publisher

Springer Nature

Published Date

ISBN 10

303075653X

ISBN 13

9783030756536

The Optimal Homotopy Asymptotic Method

Engineering Applications

By: Vasile Marinca,Nicolae Herisanu

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The Optimal Homotopy Asymptotic Method

Engineering Applications

By: Vasile Marinca,Nicolae Herisanu

This book emphasizes in detail the applicability of the Optimal Homotopy Asymptotic Method to various engineering problems. It is a continuation of the book “Nonlinear Dynamical Systems in Engineering: Some Approximate Approaches”, published at Springer in 2011 and it contains a great amount of practical models from various fields of engineering such as classical and fluid mechanics, thermodynamics, nonlinear oscillations, electrical machines and so on. The main structure of the book consists of 5 chapters. The first chapter is introductory while the second chapter is devoted to a short history of the development of homotopy methods, including the basic ideas of the Optimal Homotopy Asymptotic Method. The last three chapters, from Chapter 3 to Chapter 5, are introducing three distinct alternatives of the Optimal Homotopy Asymptotic Method with illustrative applications to nonlinear dynamical systems. The third chapter deals with the first alternative of our approach with two iterations. Five applications are presented from fluid mechanics and nonlinear oscillations. The Chapter 4 presents the Optimal Homotopy Asymptotic Method with a single iteration and solving the linear equation on the first approximation. Here are treated 32 models from different fields of engineering such as fluid mechanics, thermodynamics, nonlinear damped and undamped oscillations, electrical machines and even from physics and biology. The last chapter is devoted to the Optimal Homotopy Asymptotic Method with a single iteration but without solving the equation in the first approximation.

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476

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Springer

Published Date

ISBN 10

3319153749

ISBN 13

9783319153742

Nonlinear Dynamical Systems in Engineering

Some Approximate Approaches

By: Vasile Marinca,Nicolae Herisanu

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Nonlinear Dynamical Systems in Engineering

Some Approximate Approaches

By: Vasile Marinca,Nicolae Herisanu

This book presents and extend different known methods to solve different types of strong nonlinearities encountered by engineering systems. A better knowledge of the classical methods presented in the first part lead to a better choice of the so-called “base functions”. These are absolutely necessary to obtain the auxiliary functions involved in the optimal approaches which are presented in the second part. Every chapter introduces a distinct approximate method applicable to nonlinear dynamical systems. Each approximate analytical approach is accompanied by representative examples related to nonlinear dynamical systems from to various fields of engineering.

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403

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Springer Science & Business Media

Published Date

ISBN 10

3642227341

ISBN 13

9783642227349

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

By: Vasile Marinca,Nicolae Herisanu,Bogdan Marinca

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Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

By: Vasile Marinca,Nicolae Herisanu,Bogdan Marinca

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Solve jigsaw puzzle

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Page Count

479

Publisher

Springer Nature

Published Date

ISBN 10

303075653X

ISBN 13

9783030756536

Nonlinear Dynamical Systems in Engineering

Some Approximate Approaches

By: Vasile Marinca,Nicolae Herisanu

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Nonlinear Dynamical Systems in Engineering

Some Approximate Approaches

By: Vasile Marinca,Nicolae Herisanu

Average ratings

N/A

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Solve jigsaw puzzle

Age

Page Count

403

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3642227341

ISBN 13

9783642227349

The Optimal Homotopy Asymptotic Method

Engineering Applications

By: Vasile Marinca,Nicolae Herisanu

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The Optimal Homotopy Asymptotic Method

Engineering Applications

By: Vasile Marinca,Nicolae Herisanu

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

476

Publisher

Springer

Published Date

ISBN 10

3319153749

ISBN 13

9783319153742

Book's by Vasile Marinca

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

The Optimal Homotopy Asymptotic Method

The Optimal Homotopy Asymptotic Method

Nonlinear Dynamical Systems in Engineering

Nonlinear Dynamical Systems in Engineering

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems

Nonlinear Dynamical Systems in Engineering

Nonlinear Dynamical Systems in Engineering

The Optimal Homotopy Asymptotic Method

The Optimal Homotopy Asymptotic Method

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