Nonlinear Ordinary Differential Equations
Analytical Approximation and Numerical Methods
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Beschreibung
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.
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.
Investigates various new analytical and numerical approximation techniques used in solving nonlinear oscillators and structural systems problems Discusses many applications of analytical and numerical methods and helps to solve nonlinear ODEs Studies analytical and numerical techniques for the treatment of parameter-dependent nonlinear ODEs Presents the energy balance method, variational approach method, perturbation method, homotopy perturbation method, homotopy analysis method, simple and multiple shooting method, and a nonlinear version of the stabilized march method to solve nonlinear ODEs Includes supplementary material: sn.pub/extras
Autor*in
Martin Hermann
Themen in »Nonlinear Ordinary Differential Equations«
Adomian Decomposition Method Energy Balance Method Homotopy Analysis Method Perturbation Method Variational Approach Method Single and Multiple Shooting Method Nonlinear Method of Complementary Functions Nonlinear Stabilized March Method Analytical and Numerical Techniques for Bifurcation Problems ordinary differential equations
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“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 Rünger, zbMATH 1361.34001, 2017)
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