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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.
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.
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