A Modified Variational Iteration Method for Nonlinear Oscillators
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Q. W. Yang
,
Y. M. Chen
Abstract
A modified variational iteration method (MVIM) is proposed for nonlinear oscillators. Different from the existing VIM, the algebraic equation deduced at each iteration stage is always linear when the proposed approach is applied to conservative oscillators. Therefore, highly accurate approximations can be easily obtained. The Duffing and the van der Pol equations are presented to validate the MVIM. Numerical examples show that the presented method is valid for both weakly and strongly nonlinear oscillators. In addition, it reveals that the MVIM is equivalent to a modified Mickens iteration scheme. Furthermore, the MVIM is extended by means of an auxiliary parameter. This parameter provides us with a convenient way to control and adjust the convergence of VIM approximations when necessary.
©[2013] by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- A New Model for Plastic-Viscoelastic Magnetohydrodynamic (MHD) Flow with Radiation Thermal Transfer
- New Exact Solutions for an Oldroyd-B Fluid with Fractional Derivatives: Stokes' First Problem
- A Modified Variational Iteration Method for Nonlinear Oscillators
- Behavioral Modeling of SNFS for Synthesizing Multi-Scroll Chaotic Attractors
- Solving a System of Linear and Nonlinear Fractional Partial Differential Equations Using Homotopy Perturbation Method
- On a Problem of Nonstationary 2D Motion of Micropolar Fluid in the Half-plane Subjected to a Uniform Magnetic Field when Normal Stresses and Tangential Velocities are Given on the Boundary
- Non-equilibrium Shock Structure Calculation with High-order Modified Navier–Stokes Equations
- A New Coupled Fractional Reduced Differential Transform Method for Solving Time Fractional Coupled KdV Equations
- A New Nonlinear Integrable Couplings of Solioton Hierarchy and its Hamiltonian Structure with Kronecker Product
- Control Volume Based Finite Element Method Study of Nano-fluid Natural Convection Heat Transfer in an Enclosure Between a Circular and a Sinusoidal Cylinder
- Hybrid Modulus-phase Synchronization of Hyperchaotic Complex Systems and its Application to Secure Communication
