Nonlinear Ordinary Differential Equations

Analytical Approximation and Numerical Methods

By: Martin Hermann, Masoud Saravi

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Paperback | 27 May 2018

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328 Pages

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23.5 x 15.5 x 1.75

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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.

Industry Reviews

"Nonlinear problems in science and engineering are often modeled by nonlinear ordinary differential equations (ODEs) and this book comprises a well-chosen selection of analytical and numerical methods of solving such equations. ... the writing style is appropriate for a textbook for graduate students. The mathematical rigorous presentation includes many example ODEs and their analytical, approximate or numerical solution, which makes an interesting read for all interested in solving nonlinear problems." (Gudula R¼nger, zbMATH 1361.34001, 2017)

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