## Nonlinear Ordinary Differential Equations: Analytical Approximation and Numerical MethodsThe 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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### Contents

1 | |

2 Analytical Approximation Methods | 33 |

3 Further Analytical Approximation Methods and Some Applications | 60 |

4 Nonlinear TwoPoint Boundary Value Problems | 121 |

### Other editions - View all

Nonlinear Ordinary Differential Equations: Analytical Approximation and ... Martin Hermann,Masoud Saravi No preview available - 2016 |

Nonlinear Ordinary Differential Equations: Analytical Approximation and ... Martin Hermann,Masoud Saravi No preview available - 2018 |

### Common terms and phrases

Adomian decomposition method Algorithm analytical ansatz approximate solution assume Banach spaces bifurcation diagram bijective boundary conditions coefficient computed convergence cos(x defined determine the Solution differential equations exact solution Example Exercise following BVP formula Fredholm operator given homeomorphism homotopy Implicit Function Theorem initial condition integration isolated solutions Jacobian Let z0 limit point matrix method of complementary multiple shooting method neighborhood nonisolated solutions nonlinear algebraic equations nonlinear BVP nonlinear ODEs numerical obtain operator equation 5.11 particular solution path-following point z0 primary simple bifurcation right-hand side satisfies shooting points simple bifurcation point simple shooting method simple turning point sin(x singular points solution curve solution field solution y(x solvable solve the BVP Substituting Taylor series Theorem Tºp Tºpo Tºy transformed transformed problem unique solution vector yo(x