Constructing numerical models of noisy partial differential equations is very delicate. Our long term aim is to use modern dynamical systems theory to derive discretisations of dissipative stochastic partial differential equations. As a second step we here consider a small domain, representing a finite element, and apply stochastic centre manifold techniques to derive a one degree of freedom mo...

duffing harmonic oscillator is a common model for nonlinear phenomena in science and engineering. this paper presents he´s energy balance method (ebm) for solving nonlinear differential equations. two strong nonlinear cases have been studied analytically. analytical results of the ebm are compared with the solutions obtained by using he´s frequency amplitude formulation (faf) and numerical solu...

A new method is described for constructing a generalized solution for stochastic differential equations. The method is based on the Cameron-Martin version of the Wiener Chaos expansion and provides a unified framework for the study of ordinary and partial differential equations driven by finiteor infinite-dimensional noise with either adapted or anticipating input. Existence, uniqueness, regula...

A local moving orthonormal transformation has been introduced to rigorously study phase noise in stochastic differential equations (SDE’s) arising from nonlinear oscillators. A general theory of phase and amplitude noise equations and its corresponding Fokker-Planck equations are derived to characterize the dynamics of phase and amplitude error. As an example, a van der Pol oscillator is consid...

We generalize the method of obtaining fundamental linear partial differential equations such as the diffusion and Schrodinger equation, the Dirac, and the telegrapher's equation from a simple stochastic consideration to arrive at a certain nonlinear form of these equations. A group classification through a one-parameter group of transformations for two of these equations is also carried out.

This paper is concerned with sufficient conditions for the controllability for nonlocal nonlinear impulsivefuzzy stochastic systems in Banach space by using the concept of Mild solution. And the conditions are drive by using Sadovskii fixed point theorem, Hausdorff measure of noncompactness and operator semigroup. 1. Introduction The problem of controllability is to show the existence ofa contr...

Dynamical stochastic models of single neurons and neural networks often take the form of a system of n>2 coupled stochastic differential equations. We consider such systems under the assumption that third and higher order central moments are relatively small. In the general case, a system of 1 2 n(n13) ~generally! nonlinear coupled ordinary differential equations holds for the approximate means...

in this paper an approximate analytical solution of the fractional zakharov-kuznetsov equations will be obtained with the help of the reduced differential transform method (rdtm). it is in-dicated that the solutions obtained by the rdtm are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

in recent years, numerous approaches have been utilized for finding the exact solutions to nonlinear partial differential equations. one such method is known as the new extended (g'/g)-expansion method and was proposed by roshid et al. in this paper, we apply this method and achieve exact solutions to nonlinear partial differential equations (nlpdes), namely the benjamin-ono equation. it i...

here a posteriori error estimate for the numerical solution of nonlinear voltena- hammerstein equations is given. we present an error upper bound for nonlinear voltena-hammastein integral equations, in which the form of nonlinearity is algebraic and develop a posteriori error estimate for the recently proposed method of brunner for these problems (the implicitly linear collocation method).we al...