This paper gives an overview of the use of Polynomial Chaos expansions to represent stochastic processes in numerical simulations. Several methods are presented to perform arithmetic on, as well as to evaluate polynomial and non-polynomial functions of variables respresented with Polynomial Chaos expansions. These methods include Taylor series, a newly developed integration method as well as a ...

in this paper, we present a new computational technique for solving nonlinear fredholm integral equations of the second kind. this proposed method is based on galerkin method and is computationally very attractive. moreover, for reducing the operations in comparing similar works, we design our algorithm based on transformations of orthogonal polynomials in approximation coefficients calculating...

We develop in this work a numerical method for stochastic differential equations (SDEs) with weak second order accuracy based on Gaussian mixture. Unlike the conventional higher schemes SDEs It\^o-Taylor expansion and iterated It\^o integrals, proposed scheme approximates probability measure $\mu(X^{n+1}|X^n=x_n)$ by mixture of Gaussians. The solution at next time step $X^{n+1}$ is then drawn f...

This article is concerned with Gaussian filtering in nonlinear continuous-discrete state-space models. We propose a novel Taylor moment expansion (TME) filter, which approximates the moments of stochastic differential equation temporal expansion. Differently from classical linearization or Itô-Taylor approaches, formed for functions directly and time variable, not by using on model. analyze the...

this paper reports the results of using three empirical methods (makkink, priestley-taylor and hargreaves) for estimating the reference evapotranspiration (et0) in the semi-arid region of tensift al haouz, marrakech (center of morocco). the penman-monteith equation, standardized by the food and agriculture organization (fao-pm), is used to evaluate the three empirical methods. the obtained et0 ...

For most practical purposes, the focus is often on obtaining statistical moments of the response of stochastically driven oscillators than on the determination of pathwise response histories. In the absence of analytical solutions of most nonlinear and higherdimensional systems, Monte Carlo simulations with the aid of direct numerical integration remain the only viable route to estimate the sta...

A new Taylor series method that the authors originally developed for the solution of one-dimensional integral equations is extended to solve multivariate integral equations. In this paper, the new method is applied to the solution of multivariate Fredholm equations of the second kind. A comparison is given of the new method and the traditional Taylor series method of solving integral equations....

A Taylor matrix method is developed to find an approximate solution of the most general linear Fredholm integrodifferential-difference equations with variable coefficients under the mixed conditions in terms of Taylor polynomials. This method transforms the given general linear Fredholm integrodifferential-difference equations and the mixed conditions to matrix equations with unknown Taylor coe...