A perturbation algorithm using any time transformation is introduced. To account for the nonlinear dependence of the function, we exhibit the function f of the system in the differential equation. To this end, we introduce the transformation t t w f Te ) , ( , where f is a function that depends on t or w. The problems are solved with new time transformation: Linear damped vibration equation, cl...

The problem of nonlinear Hamiltonian oscillators is one of the classical questions in physics. When an analytic solution is not possible, one can resort to obtaining a numerical solution or using perturbation theory around the linear problem. We apply the Fourier series expansion to find approximate solutions to the oscillator position as a function of time as well as the period-amplitude relat...

A method is implemented within the context of dynamical nucleation theory in order to efficiently determine the ab initio water dimer evaporation rate constant. The drive for increased efficiency in a Monte Carlo methodology is established by the need to use relatively expensive quantum mechanical interaction potentials. A discussion is presented illustrating the theory, algorithm, and implemen...

The main idea of this paper is to demonstrate a stochastic computational technique consisting of the generalized stochastic perturbation method using the Taylor expansions of random variables and the classical Finite Difference Method based on regular grids. As it is documented by computational illustrations, it is possible to determine, using this approach, also higher probabilistic moments fo...

in this paper, we present an ecient numerical algorithm for solving fuzzy systemsof linear equations based on homotopy perturbation method. the method is discussed indetail and illustrated by solving some numerical examples.

This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work [1], a numerical method coupling an Asymptotic Numerical Method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using ...

In this paper a new method for computation of higher order corrections to the saddle point approximation of the Feynman path integral is introduced. The saddle point approximation leads to local Schrödinger problems around classical orbits. Especially, the saddle point approximation leads to Schrödinger problems around classical periodic orbits when it is applied to the trace of Green’s functio...

We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is time-limited. Spectral methods based on the commutativity of convolution, first proposed and analyzed in the 1990s, provide an elegant mathematical framewor...

More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput. 154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for the generalized Fisher’s equation to o...

In this paper, He’s homotopy perturbation method is applied to solve linear Schrodinger equation. The method yields solutions in convergent series forms with easily computable terms. The result show that these method is very convenient and can be applied to large class of problems. Some numerical examples are given to effectiveness of the method.