Nonlinear ordinary differential equations [electronic resource] : analytical approximation and numerical methods / Martin Hermann, Masoud Saravi.

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Nonlinear ordinary differential equations [electronic resource] : analytical approximation and numerical methods / Martin Hermann, Masoud Saravi.

9788132228127 (electronic book)
813222812X (electronic book)
9788132228103

New Delhi : Springer, 2016.

English

1 online resource (xvi, 310 pages) : illustrations

10.1007/978-81-322-2812-7 doi
9788132228103

QA372

515/.355

The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed May 23, 2016).

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