Nonlinear Ordinary Differential Equations: Analytical Approximation and Numerical Methods

✍ Scribed by Martin Hermann, Masoud Saravi (auth.)

• Publisher: Springer India
• Year: 2016
• Tongue: English
• Leaves: 320
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
A Brief Review of Elementary Analytical Methods for Solving Nonlinear ODEs....Pages 1-31
Analytical Approximation Methods....Pages 33-59
Further Analytical Approximation Methods and Some Applications....Pages 61-120
Nonlinear Two-Point Boundary Value Problems....Pages 121-164
Numerical Treatment of Parametrized Two-Point Boundary Value Problems....Pages 165-299
Back Matter....Pages 301-310

✦ Subjects

Ordinary Differential Equations; Numerical Analysis; Mathematical Physics; Mathematical Applications in the Physical Sciences