Homotopy Perturbation Method is an effective method to find a solution of a nonlinear differential equation, subjected to a set of boundary condition. In this method a nonlinear and complex differential equation is transformed to series of linear and nonlinear and almost simpler differential equations. These set of equations are then solved secularly. Finally a linear combination of the solutio...

An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordin...

In this work we want to describe a discrete version of the well–known Adomian decomposition method (ADM) applied to the discrete nonlinear Schrödinger equation (NLS). The ADM was introduced by Adomian [3], [11] in the early 1980s to solve nonlinear ordinary and partial differential equations. The discrete nonlinear Schrödinger equation is omnipresent [8] in applied sciences, e.g. describing the...

In the study of transverse vibrations of a hinged beam there arises a boundary value problem for fourth order ordinary differential equation, where a significant difficulty lies in a nonlinear term under integral sign. In recent years several authors considered finite approximation of the problem and proposed an iterative method for solving the system of nonlinear equations obtained. The essenc...

In this paper the problems of state estimation, tracking control and shape control in a micro-cantilever beam with nonlinear electrostatic actuation are investigated. The system’s partial differential equation of motion is converted into a set of ordinary differential equations by projection method. Observabillity of the system is proven and a state estimation system is designed using extended ...

The boundary value problem (BVP) for a class of nonlinear ordinary differential equations is examined. It can be used to describe the eversion problem for a spherical shell composed of a class of transversely isotropic incompressible Mooney-Rivlin materials. The solutions of the nonlinear equation describing the relation among deformed thickness, initial thickness and material parameters of the...

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...

In this paper we propose, a collocation method to solve unsteady gas equation which is a nonlinear ordinary differential equation on semiinfnite interval. This approach is based on generalized Laguerre polynomials and rational Chebyshev functions. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with...

In this paper we propose a Lagrangian method for solving Lane-Emden equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on a Modified generalized Laguerre functions Lagrangian method. The method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with some ...